I have had a cosmetic procedure with my moderate regurg. They were very cautious. With my cosmetic procedure they gave me the IV antibiotic drip before, during and after. Be sure to talk to your surgeon and anesthesiologist about it.
It depends on the degree of mitral regurg. If you have mild - moderate MR, it is unlikely to be problem. You are going to have to trust the judgment of the doctor that has seen your echo. Mitral valve prolapse by itself does not pose a problem.
If the MR is significant, it increases your risk of peri operative heart failure. If you doctor didn't discuss this, they must not be very concerned with your degree of MR.