I spoke to some former patients of the board-certified surgeon I have a consultation with and she said that he asks patients on birth control to stop taking pills before bc of risks of blood clots. This makes me a bit concerned that if I get my period (cycles were irregular before) on the surgery date this could cause excessive bleeding and other complications.
What your doctor said is true about blood clots but anemia before surgery is also unsafe. You have to discuss these issues with your gynecologist and your plastic surgeon. The risk versus benefit will have to be evaluated.