It would be better to say "... make contributions to" since a "contribution" is an intangible noun: it refers to an abstract concept and is not something a person could possess or "have".
(1) Some people take credit for work which they didn't even make contributions to.
A further refinement is to replace the clause "to make [a] contribution" with the simpler verb "to contribute". Here we can also remove "which":
(2) Some people take credit for work they didn't even contribute to.
You can (arguably) further improve the sentence by moving the preposition from the end of the sentence:
(3) Some people take credit for work to which they didn't even contribute.
Most modern native speakers would probably say (2). In writing, either (2) or (3) would be perfectly acceptable. Traditional writing guides suggest using (3) instead of (2) in order to avoid ending the sentence with a preposition.