I was always was taught that the number 1 rule about re-gifting was to never regift to the original gifter -- at least if you do choose to do that, let the person know and don't try to deceive...is that really petty..?
I don't think you're being petty.
The frame was part of your gift with your painting. To get it back, as a re-gift, from the person you gave it to, without some sort of explanation, is rude and thoughtless behavior on the other person's part.
I would like to return the frame but don’t want to seem spiteful or rude — what are your thoughts?
You should not return the frame. Why compound the other person's bad manners with a display of bad manners on your part?
I'm not sure that significant deception was involved. Maybe your friend was short of cash, or he was being inappropriately frugal or pragmatic in re-using the frame you gave him for his photo gift to you, and he just hoped you wouldn't notice it was the same frame, or he felt too awkward about being more upfront with you about it. But, if this is a person whose friendship you otherwise value, I'd just forget it, and chalk it up to a gauche social blunder on his part, and far from the worst thing a friend could do. He was giving you a photo as a gift and he likely didn't intend to offend you with his gift.
As far as his removing the mat from the painting you gave him, and deciding to re-frame it, I agree with what others here have said--once you give a gift, it belongs to the other person and they can do with it however they wish. Except that really shouldn't include re-gifting part of it back to you.
It may be the combination of both seeing your painting altered, and
having the frame given back to you, that got you upset--it was as though your friend wasn't sufficiently valuing the total gift you gave him, or your effort in matting it, and monetary outlay in framing it, or your choice in how you wanted your painting displayed. Well, it's his painting now, and your tastes may differ in how it looks best, and he's entitled to enjoy it or alter it any way that he wants to. If this really bothers you, don't give him another of your paintings as a gift. But, if he's a friend you want to keep, I wouldn't do much more than that. You've already let him know you were upset by his behavior, and, hopefully, he'll be more thoughtful and considerate about this sort of thing in the future.