Is what happened considered backbiting, and what must be done to atone for the sin if it is?

If the discussion about a woman is intended to warn others against her, then it is permissible backbiting. However, if it is merely for amusement, then it is forbidden backbiting. Its expiation is repentance, seeking forgiveness, and resolving not to return to it, along with seeking forgiveness for the one you backbit and supplicating for her.

Backbiting is originally forbidden, but it may become obligatory or permissible for a legitimate Sharia purpose that cannot be achieved except through it. Among the reasons that permit it are: seeking justice, seeking help to change an evil, seeking a fatwa, warning Muslims from evil, mentioning a person who openly commits sin or innovation, and identifying someone known by a specific nickname without intending disparagement.