Thomas More didn't actually give Richard Rich a gift. As Chancellor of England, one of his duties was to act as judge over civil disputes. Often people would try to bribe him to make a judgment in their favor.
When Richard Rich met with More, he was expecting to be given a high position at the king's court, but all More had to give him was a teaching position. Unhappy with that, Rich told More that he could get a better offer from Cromwell, so More told him to go ahead and do so. Then Rich notices the fine Italian silver cup, which is engraved with the words "l am the gift of Averil Machin." More tells Rich to take the cup because he certainly can't keep it; it would not be the right thing to do. When Rich grabs the cup, More asks what he will do with it, and Rich says he'll sell it to buy a new cloak. More is beginning to realize that Richard Rich is overly ambitious and tells him, "A man should go
where he won't be tempted." If he only knew just how ambitious Rich was, maybe he wouldn't have let him have that cup!