May I add one careful thought?
If a show label or registration tag is still on a frame, and removing it may damage the finish, sometimes it might be better to leave it there and let it become part of the story of the piece.
I say this because we once had an old icon in for restoration. There was a nail driven into it, and a very serious restorer explained to us, very seriously, that the nail should not be removed. It was no longer just “damage.” It had become part of the history of that icon.
Since then, that idea has stayed in my head.
Of course, this is different from a normal repair job, and the client has to agree. But sometimes a mark on a frame, especially if it came from an exhibition, is not only a defect. It can be part of the provenance.
I once bought a painting where the artist had made the frame himself out of what looked like floor trim. From a framing point of view, it was probably the ugliest frame in my little gallery. But if I had replaced it, I would have removed half the charm and half the story.
So maybe the best repair is not always to hide the wound. Sometimes it is to explain it.