I am so sorry for your loss. PLEASE get legal help if only on a consultation and letter writing basis from an attorney.  If you were left the house as part of an inheritance you can continue to pay the mortgage that is still in your Grandmother's name without having to refinance or threat of foreclosure.  Inheritance is a general exception to the "due on sale" (and inheritance falls under this) clause of a mortgage.  You can pay the loan until it is paid off.  Now, if you wish to refinance the loan you will have to do so the regular way and apply, get approved, etc.  If they continue to threaten foreclosure I would contact your state banking commission and file a complaint.  Good luck.