Should I be extra worried about bleeding when the drain is removed?

No, I don't believe that you are at increased risk of bleeding with routine post op drain removal, even if you are anti coagulated on coumadin. Your surgeon or their nurse will do this in a controlled fashion and monitor the site for a few minutes to see that you don't bleed. Good luck.

Hi. Not  at all, the removal of the drain will not cause any bleeding, is easy and painless.
International Member of the American Society of Plastic Surgeons (ASPS)
Member of the International Society of Aesthetic Plastic Surgery (ISAPS)

Drain removal is fairly easy and painless, and should not cause any additional bleeding. Often times removing the external stitch that holds the drain in place is the part the patients feel the most. I have my patients log the amount of drainage they have every 24 hours and once I think the number is low enough I will remove them. I have my patients gradually return to normal activity once the drains are removed to prevent too much fluid build up from occurring rapidly. I then have my patients return to clinic 4-5 days to ensure no seroma is present. I would recommend discussing post-drain removal directions with your Board Certified Plastic Surgeon as he may have specific instructions for you. Good luck and best wishes!

I don't think you should have anything to worry about.  We routinely remove drains in patients that are on anticoagulation medications and I've never seen a bleed afterwards.  The drain is secured by one external stitch so it should come out very easily and it would be exceptionally rare for this to cause any bleeding.  Good luck with your recovery.