Non-marital property issue in SC.

Me and my wife are going through a divorce. We bought a house in 2003 (BEFORE being married), and tried to finance it in both of our names. Her credit made our interest rate go up, so the mortgage was done entirely in my name. However when the deed was written, they still placed her name on it because of the original application. We married in 2004, and she left in 2007. She originally agreed that she didn't want anything to do with the house, and was willing to sign her name off the deed as part of the divorce agreement. However since then things have gone sour and from what i understand her lawyer is going to ask for her "interest" in the house at our mediation. What exactly does this mean? There was little to no equity in the property at the time she left, and we did not make any improvements to the house that she would have helped pay for. I know she is using the fact that the court gave her full custody at the temp hearing as leverage to milk me as much as she can (we also originally agreed on joint custody, and i'm fighting her for it). I would like to be prepared when I go to mediation. The property is in SC. Please help!!!