My "Stepfather" was married to my mother traditionally not legally, so legally he was only a close friend. When he refinanced the home, he had me sign the deed with him as Joint Tenant With Right of Survivorship, but he took on the loan alone. He didn't want us to lose the home in the event he should pass away. Unfortunately, he recently passed away and the mortgage is still there under his name. I did a quit claim deed to remove his name from the deed and in writing the new deed I had my mother added onto the deed. My mother is paying for the mortgage and we both know that since the mortgage is under my "stepfather's" name my mother can not claim the taxes. We are fine with that since it will only be about 4 more years to pay off the loan.
The question is, by adding my mother onto the deed by quit claim deed, do I need to file a gift tax. I called the IRS and they stated that the transfer I did by quit claim deed does not require a gift tax to be filed. However, they suggested I file one to protect my mother's interest in the property since there is a mortgage still out there.
If I file a gift tax, how do I calculate my basis on the property. I don't know how much he bought the property for but I can look up the current FMV on the county website. Or do I have no basis since I didn't pay anything for it and technically the bank still owns it until the mortgage is paid off?
Any information would be greatly appreciated. Thanks!

