I was baptized in the Catholic Church, raised in the Methodist Church, and became an atheist when I was about 14 years old. My grandmother on my father's side was a non-observant Jew, but my father has always been Methodist. I was circumcised as a baby, although I have no idea how long after birth it was done; I assume it was performed by a doctor, but my mother says he was Italian, and probably Catholic, not Jewish. It certainly wasn't a bris, and the doctor obviously wasn't a moyle (excuse me if I misspelled the words).
I'm not planning to convert, but I am curious as to how my circumcision would be handled if I did convert. Would the procedure need to be repeated by a moyle?