Is it ever appropriate for a gift giver to want a cut of the gift that they have already given to somebody else?
Gifting regret is a very real phenomenon. Giving a present to somebody should be a nice gesture, an act of generosity that the person receiving the gift gets to enjoy whichever way they see fit. However, there are plenty of times when a gift giver feels like their gift has not been appreciated properly, may be misused, or they decide that they actually want it for themselves. What should be a selfless act suddenly becomes a very self-interested one, and something that should be touching turns into an interaction that is nothing short of distasteful.
Perhaps there are situations where it is better for a gift to be given back in one way or another. It is possible for some gifts to be legitimate mistakes that may have real, unfortunate consequences if they aren't reversed. At the same time, a lot of people who have gifting regret are thinking about their own selfish desires more than anything else. Like a child who doesn't want to play with a toy until they see one of their friends with it, they feel like they are missing out once it's out of their hands. The mature way to go about things would be to cut their losses and move on, but that isn't always going to be a choice that they are willing to accept. It leaves the person who received the present in an awkward position.