My mom now has durable power of attorney for my father who has dementia. They jointly own their house together which is paid in full. We are wanting to use a quit claim deed to transfer the whole house to mom so she can sell it to help pay for medical and living expenses. A lawyer suggested using a quit claim deed. In filling out the quit claim deed, I am trying to figure out how to word the document so she will be tax exempt. Do I list it as a gift between family members or some kind of transfer? Mom will be serving as the grantee for dad and she will also be the grantor.

Why? She can just still sell it, when they have a buyer, she signs for her and husband to the new buyer.

You are doing a step and adding a cost that is not needed.

If she has power of attorney then there is no need to transfer the property and complicate matters. As noted she can sign off on the sale using the POA. She just signs:

Jane Doe
Under POA for John Doe.

The notary will verify the POA at the closing.