diff --git a/synapse/storage/background_updates.py b/synapse/storage/background_updates.py
index 11a1b942f..c88759bf2 100644
--- a/synapse/storage/background_updates.py
+++ b/synapse/storage/background_updates.py
@@ -242,6 +242,25 @@ class BackgroundUpdateStore(SQLBaseStore):
         """
         self._background_update_handlers[update_name] = update_handler
 
+    def register_noop_background_update(self, update_name):
+        """Register a noop handler for a background update.
+
+        This is useful when we previously did a background update, but no
+        longer wish to do the update. In this case the background update should
+        be removed from the schema delta files, but there may still be some
+        users who have the background update queued, so this method should
+        also be called to clear the update.
+
+        Args:
+            update_name (str): Name of update
+        """
+        @defer.inlineCallbacks
+        def noop_update(progress, batch_size):
+            yield self._end_background_update(update_name)
+            defer.returnValue(1)
+
+        self.register_background_update_handler(update_name, noop_update)
+
     def register_background_index_update(self, update_name, index_name,
                                          table, columns, where_clause=None,
                                          unique=False,
diff --git a/synapse/storage/registration.py b/synapse/storage/registration.py
index 3aa810981..95f75d6df 100644
--- a/synapse/storage/registration.py
+++ b/synapse/storage/registration.py
@@ -39,12 +39,7 @@ class RegistrationStore(background_updates.BackgroundUpdateStore):
         # we no longer use refresh tokens, but it's possible that some people
         # might have a background update queued to build this index. Just
         # clear the background update.
-        @defer.inlineCallbacks
-        def noop_update(progress, batch_size):
-            yield self._end_background_update("refresh_tokens_device_index")
-            defer.returnValue(1)
-        self.register_background_update_handler(
-            "refresh_tokens_device_index", noop_update)
+        self.register_noop_background_update("refresh_tokens_device_index")
 
     @defer.inlineCallbacks
     def add_access_token_to_user(self, user_id, token, device_id=None):
diff --git a/synapse/storage/search.py b/synapse/storage/search.py
index d3e76b58d..13c827cf8 100644
--- a/synapse/storage/search.py
+++ b/synapse/storage/search.py
@@ -31,6 +31,7 @@ class SearchStore(BackgroundUpdateStore):
 
     EVENT_SEARCH_UPDATE_NAME = "event_search"
     EVENT_SEARCH_ORDER_UPDATE_NAME = "event_search_order"
+    EVENT_SEARCH_USE_GIST_POSTGRES_NAME = "event_search_postgres_gist"
     EVENT_SEARCH_USE_GIN_POSTGRES_NAME = "event_search_postgres_gin"
 
     def __init__(self, db_conn, hs):
@@ -42,6 +43,16 @@ class SearchStore(BackgroundUpdateStore):
             self.EVENT_SEARCH_ORDER_UPDATE_NAME,
             self._background_reindex_search_order
         )
+
+        # we used to have a background update to turn the GIN index into a
+        # GIST one; we no longer do that (obviously) because we actually want
+        # a GIN index. However, it's possible that some people might still have
+        # the background update queued, so we register a handler to clear the
+        # background update.
+        self.register_noop_background_update(
+            self.EVENT_SEARCH_USE_GIST_POSTGRES_NAME,
+        )
+
         self.register_background_update_handler(
             self.EVENT_SEARCH_USE_GIN_POSTGRES_NAME,
             self._background_reindex_gin_search