While we generally are careful to remove all chatzitzot before immersing, after the fact, many of these chatzitzot do not actually invalidate your tevilah. Some chatzitzot will invalidate the tevilah, so it is important to ask an individual question in each specific situation.
If it was a very small piece of skin hanging off, and it wouldn't bother you to leave it, then it is not considered a chatzitzah and your tevilah remains valid. This is true even if you pulled it off afterwards.
Please feel free to get back to us with any further questions.