My cousin once went on a date with a girl that I am currently dating. I'll be explicit, it was one date, and nothing happened. The girl that he went on a date with was mine and my now ex-girlfriend's friend.
After the date my cousin became very clingy and attached to the girl, and after several advances she politely asked him to stop and told him that she was not interested. He continued his advances for quite some time, and even came to my ex-girlfriend and I to ask us to ask him to stop.
After about 4 years of dating, my ex-girlfriend and I broke-up, but the girl who my cousin dated remained my friend. She helped me through a very hard time in the 3 months after our break-up, and we ended up becoming a "thing" afterwards. We've now been dating for 4 months. The date that she went on my cousin at this point had happened over 12 months ago.
I recently came to realize that my cousin has been telling my family that this girl that I've been introducing to them is his "ex-girlfriend", although that's 100% not true. Up until I heard this, I had not cared what my family thought of the situation or what he told them, but since he is making their one date out to be much more than it really was, it has caused my girlfriend and I some frustration. Ultimately, we don't care since we are confident in our relationship and ourselves, but we don't want people to have the wrong idea/information.
How can I handle this type of situation but also avert any confrontation and conflict?