Take, for example, this question. It was migrated from SO to Programmers and the asker put a bounty on it.
Now I see the "remove post notice" option in the mod tools, but there is no moderator-only notice. I haven't tried it (even for science) to see if it'd remove, the migration banner, the bounty banner, or nothing at all, but it seems that the option should not be enabled in the first place.
This may be related to this issue from a couple weeks ago.
See Shog9's answer and comments on it for more details. Looks like it's possible to add a bounty notice to a post that already has a mod notice and both notices are shown as expected. But using the "remove post notice" option on a post like that removes both the mod notice and the bounty notice. I think "remove post notice" should only affect the moderator notice.