It depends on your risk of getting pregnant if you are not on the pill. If you can use a condom or abstain from vaginal intercourse for 4 to 6 weeks before the surgery, then please do STOP the birth control pill, birth control patch, birth control ring 4 to 6 weeks before a surgery.
A paper from 1988 shows: that research from the 1970s (when women were on HIGHER doses of estrogen) that 0.19% of women on the pill versus 0.035% NOT on the pill got a deep vein thrombosis after surgery. Other studies showed: 4.6% of patients who underwent gynecological operations for benign disease, 0 of 99 patients who underwent various abdominal operations, and 20% in 33 patients who had emergency appendectomies had a thrombosis.
From the American College of Obstetrics and Gynecology in 2018: No trials exist to demonstrate a reduction in postsurgical VTE with preoperative discontinuation of hormone therapy, and this practice should not be routinely recommended. In women using combined oral contraception, prothrombotic clotting factor changes persist 4–6 weeks after discontinuation, and risks associated with stopping oral contraception a month or more before major surgery should be balanced with the very real risk of unintended pregnancy. It is not considered necessary to discontinue combination oral contraceptives before laparoscopic tubal sterilization or other brief surgical procedures. In current users of oral contraceptives who have additional risk factors for VTE having major surgical procedures, heparin prophylaxis should be considered.