In what way does Hester acknowledge her sin to Pearl?

Pearl asks her mother to tell her a story about the Black Man, who is said to haunt the forest. The Black Man is a myth about the devil, and the story says that he carries a large book and pen with which people write their names in blood. The Black Man then puts his mark on the person.

Hester, tired of Pearl asking about the scarlet letter, tells her that the letter is the mark of the Black Man, which she received after meeting the Black Man once before.