Flirting at work

Hey guys so I need some advice on what too do . My boyfriend and I have been dating almost 8 months now and he works at chick fi la. For the past month this girl has been flirting with him like not super super bad so it really hasn’t bothered me because I trust him I still trust him but, these past few weeks she has gotten way way way worse and to add in she knows we are dating because she has seen us come in chick fi la and go thru the drive thru and he has said stop I have a girlfriend and when she does flirt he doesn’t respond. Anyways so these past few weeks have been getting way worse for example last week she flirted with him the whole time like he would say my pleasure and she would be like i want it too be your pleasure and she would calling him hot like the food and calling him babe sticking her butt out which if you ask me is super inappropriate for the work place and she will walk him out to his car and he would get in but she is rubbing all up on saying your so hottt like your car and he would be like I have too go and it’s been this bad for two weeks!! He asks me not to message her because he does not want drama and I completely understand that but he doesn’t want too tell a manager because he doesn’t want drama so I really don’t know what too do at this point like do I message her or what? Am I being too jealous or protective or anything like that but then again it has been going on for over a month. What do y’all think I should do or do you think I’m just being too protective or jealous ?