Tell her to ask for proof!

You quickly whisper into your GFs ear: “Proof! Ask her to get some proof first!”

My GF nods and says: “ Maybe you should get some proof first. His girlfriend would probably think that you are lying. Do you think you can get some?”

M responds jokingly: “Well I mean...probably”

My GF: “Maybe next time in the gym you can make a picture of him staring at you! Or make a secret video when you guys talk.”

M responds: “Alright, if you say so.”

Nice. All you have to do now is avoid staring at her at all cost.