The publishers don’t get paid to run those “ads” on books. Normally they request the use of it from the film/tv company as it drives sales of the books, and the film/tv doesn’t mind the extra exposure.

In theory they’d stop using the sticker once they release the new official tie-in artwork cover to the tv/show when it’s out. However, when it’s a series, that new cover usually only applies to book one so the rest of the books with often still get stuck with the sticker!