If I'm not wrong, "rumor" means:
A story or report of uncertain or doubtful truth
and "unfounded" means:
Having no foundation or basis in fact
If so, what is the difference between an "unfounded rumor" and a "rumor"?
A rumor might be true or untrue. Even if it's untrue, though, it might be based on fact:
In contrast, an unfounded rumor would be based on no credible supporting evidence:
(Alice and Bob could have been talking about anything; Alice may have simply dropped a pencil, and Bob was handing it back to her. They may not even know each other's names! That looks like the birth of an unfounded rumor.)
A rumor is uncertain or doubtful (but may be true). An unfounded rumor has no foundation or basis in fact (and thus cannot be true).