Because forgiving is a moral virtue, you talk of gift-giving as part of the process. How big of a gift are we talking about. Should I pay for the person’s medical bills, for example? Would paying for someone’s housing be over the top?
The gift-giving is always in the context of the forgiver’s capacity and the quality of the relationship at the moment. I noticed that you gave two examples regarding money. In actuality, the gift need not be monetary or even something physically concrete wrapped in a package. For example, a smile might be a great gift if such smiles have been non-existent for some time. A returned phone call might be just what the other needs. I think the gift-giving needs to be in the context of the moral virtue of temperance, or something that is balanced and reasonable and not “over the top” for a given forgiver.