(E) is not correct because appointing Lee head of the arts commission doesn't have to be the ONLY way to repay him. Even if there were other ways to repay Lee, the mayor could still want to do it by appointing him head of the arts commission.
(D) is, oddly enough, irrelevant. After all, the argument is about the mayor appointing Lee based on previous favors. Even if Lee's qualifications WERE relevant to the decision, it has no bearing on this argument.