Do I bring something I don’t really care about?

Long story short, annoyingly a new colleague has come and given new life to the world of gossip to the point where I am now the target and I guess because I don’t get super personal, go to all the socials etc. They pinned me as anti-social or I hate everyone but it’s a lie.

Im just a quiet, spoken when spoken to and generally trying to pick the slack of an entire region in anyway I can kind of person

But anyways, my colleague like a child ran to my manager with some lie and my manager said “do you and x have an issue” I said no

He said that he’ll bring it up to the person etc but that didn’t happen. I could care less. I feel like I could work with someone who hates me as long as I’m being paid but should I tell my manager I don’t like how he as a MANAGER handled the situation but I also don’t want to seem like I have the issue when it’s actually my colleague who should of been a human being and had a chat with me