According to How does the bounty system work?, questions with bounties are removed from the "featured" tab once the bounty ends:
Questions with an active bounty appear with a special icon in all question lists, and are also visible on the home page's Featured tab.
During the grace period, there will be no indication in the questions lists (e.g. front page, featured tab) that the question has a bounty
However, the current behavior, at least in some instances, is that bountied questions are remaining on the featured tab beyond the seven-day bounty period.
On Biblical Hermeneutics.SE, a recently bountied question's revision history shows that the bounty ended two days ago (July 26, 08:47 UTC) and that it started on July 18 at 07:00 UTC:
Given this, the question should have been removed from the featured list on July 25, at the start of the grace period. As of this moment, however, the question still appears on the featured tab:
The problem is not limited to BH.SE. On Christianity.SE right now a question whose bounty was started more than 7 days ago, and which was already awarded, still appears in the featured tab:
Why are bountied questions not being removed from the featured tab exactly 7 days after their bounties start?