See how Solomon treated the two prostitutes who came to him for judgement?
See how Jesus treated the woman taken in adultery when the pharisees wanted judgement?
Will YOU take up the rock and throw it at her?
AGAIN...she is NOT a woman at the well or a woman caught in adultery. Those women were NOT members of the Church.
So since she claims to be a member of the church...the question REALLY is: Will YOU FOLLOW the scripture and "Purge the evil person from among you."?
Again...and its VERY clear in the NT...if the woman at the well had been a member of the Church of Corinth...she would have been handed over to Satan for the destruction of the body until such a time she repented. Do you REALLY not see that?