Should I tell my boyfriend about a troublemaking friend ?

My boyfriend recently moved in and I have encouraged him to make friends in the area. (he previously lived in the next state) He recently told me that he befriended a co-worker, who I’ll call “Tom”.

It turns out Tom was the best friend of my previous partner, and Tom’s “inference” was a large part of our relationship ending. He would tell my ex-partner things about me that were either exaggerations or half-truths. For example: I was at dinner with a co-worker one night, and Tom told my partner that he saw me out with another guy and we looked ‘cozy’ (it was a co-worker, and we are friendly, but not THAT friendly).

Another friend, Mike, who recently broke up with his boyfriend, told me that Tom is the roommate Mike’s ex-boyfriend. My friend explained that Tom was part of the reason that they broke up.

While it’s been years since I’ve seen or talked to Tom, and I don’t want to discourage my boyfriend from making new friends, this concerns me. Our relationship is strong, and I feel that my boyfriend trusts me (he has no reason not too), but should I say something to him about Tom ?