I don't think that currently there is a feature which automatically notifies the users (Correct me in your answers if I'm wrong here).
So, it seems there are only two plausible solutions:
The users have to come repeatedly back to all of their answers and manually do the checking (This is of course absurd and not a solution at all IMO).
The Moderator, who has added the banner/notice, should always leave a comment under the answer telling why the notice has been added and what the user is required to do to get it removed.
But, unfortunately, that is not happening all the time (That is why this post).
If such being the case, the very purpose of adding the notices will get defeated.
- How will the users know that a "citation required" banner has been added to one of their answers?