OP
Coming from a Jesuit undergrad school myself, here is my take on your question. If you do not know anything about the Jesuit ideals and traditions, then do not bring it up in your essays. Jesuits do not focus solely on the religion itself, but rather have a very specific set of ideals and standards for education and service, and if you are not prepared to talk about them specifically, I would stray away from the subject.
That being said, if your specific religion HAS played a large part in your decisions to become a physician or apply to the specific school, then mention it and describe how. I think that saying how a certain teaching has affected your life is more important than simply stating which religion you are. But make sure that anything you talk about in your essays you are prepared to talk about in an interview.
Hope that helps!