When the featured tag is removed from a question, the question is bumped, as with any other edit. I propose that, when that is the only change to a question, it not be bumped: the point of detagging is to call attention away from the question, and bumping the question defeats that purpose.
Note that there's an outstanding feature request for retagging not to bump (and another), and one for mod edits optionally not to bump, but this is more specific than either of those, and where public policy may dictate those be denied, this may be worth granting anyway.