Do you need to file a quit claim deed to remove someone from the mortgae loan who is not on the deed or the deed of trust?

A deed of trust and mortgage for most purposes are the same thing. If a person is not an owner of property, or a co-owner, so that their name is not on the deed and they didn't inherit an interest, then there's nothing for them to quitclaim. If a person signs the note, the document where it is agreed to pay the lender the loan amount plus interest, only the lender can release them from liability, usually done by a document simply entitled "release", or a "certificate of partial release".