The Ignore Icon in FTM web merge is a toggle. It does nothing to the current display.
Once turned on, you should not see the item again as a hint in FTM. It may still show in Ancestry, or reappear if they change the database.
Most of the time I do not see the item again when I do a search, however sometimes it still shows up. Not sure why or when. Ignore does seem to work most of the time on hints. Anyone have other experiences?