does quick claim deed effect your mortgage

My grandmother and I bought a house last month. My grandmother has lived with me for the last year. She bought the house "with me" so that I could qualify for the loan. My grandmother is 89. I am the one that pays the mortgage. I am trying to find the best way to make sure that I can keep my house in the event something happen to her. I understand that I may have to spend a lot in probabate for a will. Also, I heard that medicare may try and get money from the house if she is on the deed. I was wondering if the mortgage can stay in both our names is she is taken off the deed. If she does a quick claim will that jeopardize my mortgage?