The problem I see is that for the women I know who wear a head covering, they see it as a pious devotion - similar to let’s say wearing a brown scapular. If the priest asked her to take off her brown scapular because the strings were visible and he didn’t want all parishioners thinking that they had to wear brown scapulars, I think her feeling would be similar. I feel sorry for her. I have never worn a head covering, but if my priest asked me to remove my scapular I would have a serious internal struggle. My whole point is that this is not a triviality to her and she therefore has my compassion. OP, phoage, I wrote you and your wife down in my prayer book.