I'm not aware of a meaning that means "to give restrictively."
Skimp means to scrip, as one "skimps on luxuries while one is scrimping and saving for a big occasion."
One might say a portion is "skimpy," or that a contribution is "skimpy."
So maybe that is what you mean by "to give restrictively."
E.g., one might say, "Mr. Jones is usually very generous with hi