The remark you regret may have occupied the other person for far less time.

Your own words stay with you far longer than they stay with anybody else. What you have replayed forty times may have been heard once, taken lightly and forgotten by evening, because everyone is mostly occupied with their own day. That is not permission to be careless, and it is a reason to hold the replaying loosely. Regret exaggerates the size of its audience.

If it genuinely warrants repair, apologise once, simply and specifically, then let it be finished. If it does not, notice how much of the discomfort is rehearsal rather than anything still happening between you. Ask, if you must, rather than keep guessing.