The issue is her not him. Of course he wants to screw your girl; you're pursuing the best things in life, you're more confident, and she's undobutedly a great catch.
She needs to calm this loser down. Tell her to tell him to cut the ****--if you think it's disrespectful to you--or you'll do it for her. This sets some boundaries as a man you have to set within and without the relationship. I'm sorry, chicks are funny. THey'll hook up with the friend or the pursuer if you're not careful. And if you don't want that, you need to deal with it. If she is unwilling to go to bat for you then you may want to dump her and not follow up on the original threat; after all, if she's a disrespectful ***** at heart, then maybe she belongs with this guy.
Supposing she is on your team here, how do you deal with him? Just like the alpha dog. Get in his face. Calmly tell him to stop, that you find it disrespectful, and that you're not going to let him cause you and your girl any trouble. This is especially useful after she told him to get lost. And be prepared to beat the **** out of him. Most of these little weasely interlopers are wimps at heart, but if he's not you must throw down for your self respect.