diff --git a/.github/workflows/scripts/strip-non-invoking-markup.sh b/.github/workflows/scripts/strip-non-invoking-markup.sh
index 65f2529..099942b 100755
--- a/.github/workflows/scripts/strip-non-invoking-markup.sh
+++ b/.github/workflows/scripts/strip-non-invoking-markup.sh
@@ -70,6 +70,51 @@ function run_len(s, ch,   n) {
   return n
 }
 
+# Whether `bare` is a CommonMark thematic break: three or more of a single one
+# of `- * _`, with only spaces or tabs between. Written as a character count
+# rather than a regex because the POSIX ERE that awk uses has no backreference,
+# so a same-character-repeated pattern (a `\1` in PCRE) silently never matches.
+function is_thematic_break(bare,   ch, i, c, n) {
+  ch = substr(bare, 1, 1)
+  if (ch != "-" && ch != "*" && ch != "_") return 0
+  n = 0
+  for (i = 1; i <= length(bare); i++) {
+    c = substr(bare, i, 1)
+    if (c == ch) n++
+    else if (c != " " && c != "\t") return 0
+  }
+  return (n >= 3)
+}
+
+# Whether `bare` is a setext heading underline: a run of only `=` or only `-`,
+# trailing spaces/tabs allowed. This is a *heading* underline only when the line
+# before it is paragraph text, which the caller tracks separately -- the same
+# characters are otherwise a thematic break (`- * _`, >=3), a list marker, or
+# ordinary text. CommonMark makes the two underline characters symmetric, and an
+# indented code block opens after either with no blank line, so the `-` case
+# that `is_thematic_break` already covers for >=3 dashes needs its `=` twin here
+# (plus 1-2 dash underlines, which are not thematic breaks).
+function is_setext_underline(bare) {
+  return bare ~ /^=+[ \t]*$/ || bare ~ /^-+[ \t]*$/
+}
+
+# Whether this line is a leaf block -- an ATX heading or a thematic break --
+# after which an indented code block may begin with no blank line. `bare` is the
+# line with its indentation removed, `indent` its width. These two shapes need
+# no context; a setext underline also qualifies but only after paragraph text,
+# so the caller handles it. A list item deliberately does NOT qualify: an
+# indented line after one is a list continuation, not code, and stripping it is
+# the over-stripping error the mention gate must avoid (the list-continuation
+# cases added in #345 guard exactly this). Both shapes are only valid at three
+# columns of indentation or fewer; deeper, they are themselves code.
+function heading_or_break(bare, indent) {
+  if (indent > 3) return 0
+  # ATX heading: 1-6 `#` then a space/tab or end of line.
+  if (bare ~ /^#{1,6}([ \t]|$)/) return 1
+  if (is_thematic_break(bare)) return 1
+  return 0
+}
+
 # Replace every closed inline code span in `text` with the placeholder.
 #
 # This runs once over the WHOLE remaining body rather than per line, because a
@@ -121,7 +166,8 @@ function strip_spans(text,   out, i, n, run, j, closerun, found) {
 BEGIN {
   in_fence = 0; fence_char = ""; fence_len = 0
   in_icode = 0
-  prev_blank = 1        # start of input behaves like a blank line
+  prev_opens_icode = 1  # start of input can open an indented code block
+  prev_para = 0         # ... but is not itself paragraph text (no setext under it)
   kept = ""; nkept = 0
 }
 
@@ -142,23 +188,26 @@ BEGIN {
         substr(bare, run_len(bare, fence_char) + 1) ~ /^[ \t]*$/) {
       in_fence = 0
     }
-    prev_blank = blank
+    prev_opens_icode = 0; prev_para = 0
     next
   }
 
   # --- indented code block ----------------------------------------------
-  # Four columns of indentation after a blank line opens one, and it runs
-  # until a non-blank line dedents to three columns or fewer. The blank-line
-  # precondition is what keeps an indented *list continuation* out of this
-  # branch: those follow their list item directly, so over-stripping them
-  # would drop a genuine request, which is the expensive error for the
-  # mention gate sharing this script.
+  # Four columns of indentation opens one when the preceding line does not leave
+  # an open paragraph or list for it to lazily continue. `prev_opens_icode`
+  # carries that from the previous iteration: it is set for a blank line, an ATX
+  # heading, a thematic break (`heading_or_break`), or a setext underline sitting
+  # under paragraph text. It runs until a non-blank line dedents to three columns
+  # or fewer. The precondition is what keeps an indented *list continuation* out
+  # of this branch: those follow their list item directly, so over-stripping them
+  # would drop a genuine request, which is the expensive error for the mention
+  # gate sharing this script.
   if (in_icode) {
-    if (blank || indent >= 4) { prev_blank = blank; next }
+    if (blank || indent >= 4) { prev_opens_icode = 0; prev_para = 0; next }
     in_icode = 0
-  } else if (prev_blank && !blank && indent >= 4) {
+  } else if (prev_opens_icode && !blank && indent >= 4) {
     in_icode = 1
-    prev_blank = blank
+    prev_opens_icode = 0; prev_para = 0
     next
   }
 
@@ -167,17 +216,30 @@ BEGIN {
       fence_char = lead
       fence_len = run_len(bare, lead)
       in_fence = 1
-      prev_blank = blank
+      prev_opens_icode = 0; prev_para = 0
       next
     }
-    if (lead == ">") { prev_blank = blank; next }
+    if (lead == ">") { prev_opens_icode = 0; prev_para = 0; next }
   }
 
   # Kept lines are buffered rather than printed, so the span scan below can
   # see across line boundaries.
   kept = (nkept == 0) ? line : kept "\n" line
   nkept++
-  prev_blank = blank
+  # Decide what the NEXT line inherits. A blank line, an ATX heading, or a
+  # thematic break (`hd`) opens an indented code block after it with no context;
+  # a setext underline does too, but only when it is actually *consumed* as one
+  # -- a `=`/`-` run (`ul`) sitting under paragraph text (`prev_para`). A ul-shaped
+  # run with no paragraph above it is not consumed: CommonMark makes it an
+  # ordinary new paragraph, so `prev_para` must go to 1 for the next line (a later
+  # underline could underline it), which is why `prev_para` keys on `consumed`
+  # rather than the raw `ul` match. Otherwise a chain of underline-shaped lines
+  # (`===` / `===` / indented request) mistracks state and under-strips.
+  hd = heading_or_break(bare, indent)
+  ul = (indent <= 3 && is_setext_underline(bare))
+  consumed = (ul && prev_para)
+  prev_opens_icode = (blank || hd || consumed)
+  prev_para = (!blank && !hd && !consumed)
 }
 
 END {
diff --git a/.github/workflows/scripts/tests/run-strip-non-invoking-markup-tests.sh b/.github/workflows/scripts/tests/run-strip-non-invoking-markup-tests.sh
index ab4b037..22a5966 100755
--- a/.github/workflows/scripts/tests/run-strip-non-invoking-markup-tests.sh
+++ b/.github/workflows/scripts/tests/run-strip-non-invoking-markup-tests.sh
@@ -167,6 +167,61 @@ check "indentation without a preceding blank line is not code" \
   $'some prose\n    @claude review' \
   $'some prose\n    @claude review'
 
+# An indented code block also opens after a thematic break or an ATX heading
+# with no blank line: neither leaves an open paragraph for the indented line to
+# lazily continue (CommonMark 0.31.2, "Indented code blocks"). A request quoted
+# this way must still be stripped (gha#356).
+check "indented code block opens after a thematic break" \
+  $'---\n    @claude review' \
+  '---'
+
+check "indented code block opens after an ATX heading" \
+  $'## Accepted phrasing\n    @claude review' \
+  '## Accepted phrasing'
+
+check "indented code block opens after a spaced thematic break" \
+  $'* * *\n    @claude review' \
+  '* * *'
+
+# A list item is NOT such a predecessor: an indented line after it is a list
+# continuation, not code, so it must survive -- and a lone-dash item must not
+# be mistaken for a thematic break, which would over-strip a genuine request.
+check "indented line after a list item is not code" \
+  $'- a point\n    @claude review' \
+  $'- a point\n    @claude review'
+
+# A setext heading underline (a run of only `=` or only `-` under paragraph text)
+# is also such a predecessor. CommonMark makes the two underline characters
+# symmetric; the `-` case is caught by the thematic-break check only for >=3
+# dashes, so the `=` twin and the 1-2 dash underlines are handled here.
+check "indented code block opens after an = setext underline" \
+  $'Heading\n======\n    @claude review' \
+  $'Heading\n======'
+
+check "indented code block opens after a single-dash setext underline" \
+  $'Heading\n-\n    @claude review' \
+  $'Heading\n-'
+
+# But a run of `=` NOT under paragraph text is an ordinary paragraph, not a
+# heading underline, so an indented line after it is a lazy continuation, not
+# code -- stripping it would drop a genuine request.
+check "= run at start of input is a paragraph, not a setext underline" \
+  $'======\n    @claude review' \
+  $'======\n    @claude review'
+
+check "= run after a blank line is a paragraph, not a setext underline" \
+  $'intro\n\n======\n    @claude review' \
+  $'intro\n\n======\n    @claude review'
+
+# A chain of underline-shaped lines: the first `===` has no paragraph above it so
+# it is an ordinary paragraph, and the second `===` then underlines it into a
+# heading -- after which the indented request is code and must be stripped. This
+# only works if paragraph state tracks whether a line was actually *consumed* as
+# an underline, not the raw match.
+check "chain of two = runs forms a heading, stripping the indented request" \
+  $'===\n===\n    @claude review' \
+  $'===\n==='
+
 check "CRLF endings are normalized" \
   $'@claude review\r\nthanks\r' \
   $'@claude review\nthanks'
diff --git a/changelog.d/strip-non-invoking-markup-block-predecessors.fixed.md b/changelog.d/strip-non-invoking-markup-block-predecessors.fixed.md
new file mode 100644
index 0000000..102e21c
--- /dev/null
+++ b/changelog.d/strip-non-invoking-markup-block-predecessors.fixed.md
@@ -0,0 +1,14 @@
+- **The `@claude review` matcher no longer fires on a mention quoted as an
+  indented code block that opens after a heading or a thematic break**
+  (gha#356).
+  `strip-non-invoking-markup.sh` only opened an indented code block after a
+  blank line, but CommonMark bars an indented block only from *interrupting a
+  paragraph* -- after a thematic break, an ATX heading, or a setext-heading
+  underline it opens with no blank line at all.
+  So a request quoted under a `---` or a `#`/`===` heading rendered as code on
+  GitHub yet slipped through the stripper and dispatched a review off quoted
+  text -- the same class of false dispatch the code-span and fence handling
+  already close.
+  A list item is deliberately still not treated as such a predecessor: an
+  indented line after one is a list continuation, not code, so stripping it
+  would drop a genuine request in the mention gate that shares this script.