Dealing with trainer BF's flirtatious client.

Hi pals! I am new here so I apologize if this is off-topic... I really need some neutral advice from fellow fitness buffs on how to deal with my gym owner boyfriend's flirtatious female client. I'm a naturally jealous person so I need other's feedback on what to do.

Long story short, I'm 25 and have been in a serious relationship for 2 years. Relationship is very stable and happy. My SO and I communicate very well and basically tell each other everything. My BF and his 2 partners opened their own CrossFit box/PT gym 5 months ago. At the time, BF was training at a different CrossFit box where he became friends with the other members. A female member *Mary asked if she could come train at BF's box when it opened and he said yes, no problem. She had his cell phone number from when they used to train together.

Mary started coming to BF's gym (I work out there too and am constantly there). From the beginning, I got weird vibes from her. She never said hello to me or acknowledged me in any way. Whatever - that's fine. Mary is 35 and just broke up with her boyfriend. After the breakup, she constantly started texting my BF about the most mundane things. She would initially start a conversation by asking him something diet/fitness related but then segue into non-related topics. A little weird, but I figured maybe she was just lonely. Boyfriend didn't answer her texts anyway unless they were fitness related. I was weirded out her friendliness so I brought it up to him. It turned into a fight but me and BF resolved it. He said he didn't think the texts meant anything but he would address with her and tell her not to text him outside of "business hours" or if it's not gym related. He also said he would address her not saying hi to me since that bothered him too. I told him not to worry about it as I didn't want to cause issues with him and a client. The business just opened and they really needed members/money.

This past month, things got weirder. Mary started bringing boyfriends GIFTS. He mentioned he liked this certain kind of cashew milk and tea. She bought it for him and brought it to the gym. I told BF this made me uncomfortable and he told me he would address it. I told him it wasn't a big deal, maybe she was just being friendly. A few days later, I was at the gym with boyfriend and he mentioned he wanted a toothbrush to keep at the gym. Mary said, "Oh I'll bring you one!" We thought she was joking. Lo and behold, the next day she brought a toothbrush (I'm not kidding). She also brought this very expensive jump rope. She told BF that she had bought one for herself and thought he would like one. He didn't accept these gifts - he told her (very nicely) to stop buying him gifts. She said she understood but brought him another gift the next day (a protein shaker) claiming it was for the gym. He told her to take it home.

BF acknowledges Mary is super inappropriate. He told me he is going to ask her to find another gym and refund her money as her actions are disrespectful to our relationship. However, I don't want him to lose money or business over her stupidity. Also, Mary seems to have finally gotten the hint. I am still uneasy around her as I think it is just a matter of time till her over-the-top friendliness
starts again. Should I just swallow my pride and be nice to her when she is at the gym? Or should I just let BF cut her loose? My gut says to be the bigger person but it's hard when someone has so blatantly disrespected me and my relationship.

What do you guys think?!