Davos confronted Melisandre about burning Shireen.
With Jon Snow as a witness, Davos forced Melisandre to confess to burning Shireen Baratheon at the stake. Davos asked Jon to execute the Red Woman, but since he owed her his life Jon simply banished Melisandre instead.
Jon told Melisandre to ride south, and warned her that if she ever returned to Winterfell she would be hanged as a murderer.