The house should have been probated. You should seek the services of an experience probate attorney. Title has to be transferred and the method of that transfer will depend upon many facts not given here. You cannot simply have a mortgage put in someone else's name.
What is not clear is who holds title. It sounds like title is still in your grandmother's name. That has to be changed. Most likely probate will be necessary to do that. You need to consult a probate attorney.
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There are at least two parts to this. First, title to the property is likely in her name or perhaps even her name and a previously deceased spouse or other party. That will need to be addressed before much of anything can be done with the property. It is possible that at this time an attorney experienced in probate and real estate will be able to help without having to file a probate case, but deciding that will depend on the facts.
As far as getting her name "off of the mortgage," generally there is not a way to do that. Instead, the new owners will have to find funds, probably through financing, to pay off that loan. The risk without resolving this is that the mortgage company will take action against the property to protect its investment. Often, as long as the payments are coming, they will not do anything, but you really have a tenuous situation with a loan obligation remaining for someone who has passed.
I am sorry for your loss.
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