Best way to deal with GF’s beta close friend?

Long story short, I like my girl. She has good qualities, she’s honest and works hard. Blah blah. She’s cool.

Me on the other hand, I’m honest, focused, I put myself and my goals first. Because of this, I don’t spend a lot of time with my girl. She always wants more of my time but she damn well knows why I won’t be able to provide that to her at this point in my life.

My girlfriend is too loyal. Cries to me anytime she gets hit on and feels that she didn’t tell them off hard enough. She’s from a part of the world where when you have a man, your man gets all your attention and you don’t flirt around. My girl has literally never really pissed me off. I’m a happy dude who’s always smiling and talking to everyone.

Now, I have hurt my girls trust a number of times. I’ve never cheated, and I’m honest, but the way I interact with other females is difficult for my girlfriend to deal with. At the end of the day, I’ve hurt her trust with a number of inconveniences over the past two years. She has serious issues forgiving me, and despite loving me, she hangs onto little things that I do.

Enter beta. To be honest, I like him when he’s around. He’s a nice guy, easy to get along with, nerdy, a good addition to a friend group.

This guy previously (and still is) completely in love with my girlfriends SISTER, who is about the same age as my girl. Long story short, this guy had a solid chance and beta cucked himself right out of an opportunity with the sister. Now, I talked to him numerous times about what to do, no avail, wouldn’t listen. So this guy hangs around as a friend (after being told it’s never gonna happen) with the sister. It’s been over a year since any romantic action occurred with the sister. Since then, he’s always available to the sister and my gf.

The sister has since got a man, and as such has no need to entertain the beta. Rather than go his own way, he uses his pre-established friendship with MY gf in order to hang around the house. As the sister gets more distant, he spends more time with my gf. My girl doesn’t hang out with a lot of her friends, she tends to prefer being alone, but since beta is nice and so available, why not?

He’ll assist her at work, he’ll play video games w her, talk to her about her problems, basically all the stuff a gay best friend would do.

I’m starting to get suspicious of his motives because I can see he’s been getting in my GF ear about my past mistakes with my gf. He validated the overwhelming (and frankly overblown) negative emotions that my gf has toward me and uses them to ignite her emotions and make her upset with me. Basically he’s been getting in her ear to get me to leave, but then is nice to my face and basically bends over whenever I’m around and he’s around.

I really don’t care too much, but it’s definitely becoming an inconvenience as my girl spends more time upset. I know she’d never give this guy a shot anyway because... beta.

I could talk to either of them maturely, I could physically crush this guy (not that it matters), and he’d never say anything to my face.

Should I care, continue to not give a shit, or should I jump in and try and throw shit upside down?

Thanks ATRP.

TLDR: Beta best friend who is failed lover of my GF sister is now trying to spend all his time with my GF as her friend, and is getting in her ear because I don’t have time to entertain a woman 24/7. Wat do?