Not much you can do tbh. If there's really nothing inappropriate going on between you and G, then this is something that your girlfriend either needs to deal with, or walk away from.

For what it's worth, I've sort of been in your shoes. A friend of mine is a guy that I've known for about the same amount of time I've been dating my partner (around 7 or 8 years), and said friend is in a famous band. (He doesn't have like, household recognition himself; if I said "I know name," people would probably say, "Who?" But if I said, "I know a guy from band," they'll likely know the band.) He's a cool guy and I'm grateful for his friendship. But my partner was definitely somewhat insecure about this when I first met my friend, likely because of the way we met (Internet, and he invited me to see his band when they next came into town - it was all platonic, though) and the first few times I met up with my friend, my partner couldn't come for some reason or another (the first time I took my best friend, who is a super fan of the band, the second and third time my partner was on tour with his band).

The important thing, though, even though my partner was a lil' insecure about it, was that he still trusted me. And when he was finally able to come with me to meet up with my friend, I introduced them and they got along great. I'm also very transparent about my communication with my friend - if we make plans to meet up, my partner knows about it before it happens. Now I can travel to another city to see my friend on tour and get dinner with him, and my partner doesn't care. It just took a little effort on my part to get him to that level of security within our relationship.

I would expect the same level of understanding and transparency with my partner if he made a new female friend, famous or no. The thing with people that are "famous" is that there does tend to be an extra level of trust and understanding that comes with that friendship, both between you and that person and with a significant other in your life - it can just be a weird thing.

I don't know if any of that even made sense, I'm just one-handed typing while eating food at my desk, lol.