We had given a gift to him should also be a correct answer. Reported

Are "gift" and "present" interchangeable here?

What is the difference between "we had given him a gift" and "we have given him a gift"? Does it have anything to do with "singular" & "continuous" tenses, i.e. "we had given" would imply giving once, whereas "we have given" would imply giving an unlimited number of times? Thank you!

Why not present?