When someone says that you treat her like scarlet letter, then it means that you treat her like an adulterer. This is in accordance with the book Scarlet Letter, where the character Hester is made to wear letter "A" to signify adulterer. It could also mean being treated as an outcast due to one's behaviors. Find out more from http://www.sparknotes.com/lit/scarlet/section4.rhtml.
In the book The Scarlet Letter, the protagonist is accused of being an adulterer. She has a big red letter A sewn to the front of all of her clothes. The people in the town shun and abuse her. So if you were treated like you had a scarlet letter you would be shunned and treated like you had broken the law or sinned.