Not sure if such a phrase or word to describe a person/actions actually exists. Have been using “to lord something over someone,” but this might not be the correct usage.
ex1: If someone pays for a vacation and subtly reminds you that they paid for everything when a choice of activities becomes a split decision, especially when the holiday has already commenced and there is no return/exit. This renders the original gift of paying more of a burden than an actual no strings attached gift.
ex2: person receives a gift of a new device from children and gives the older model to spouse, but when spouse tries to exercise control over older device the person reminds them that it is/was theirs and should still have power over it.
perhaps a guilt trip, but especially with monetary/possessions used to influence and hold something over someone.