My dad has dementia and his girlfriend wants to marry him. Could she change the trust that is already written?

A diagnosis of dementia doesn't , all by itself, make someone legally incompetent. Until your father is determined to be legally incompetent, he can change his mind on legal papers. A consultation with the lawyer who drew up the trust is a very good idea. And a pre nup.

Your father cannot get married. He has to be able to make an informed decision. If a irrevokable trust she can't do a thing. Not sure about a revocable one. I don't think POA responsibilities cover that. Just like a Will, no one can change it but the person who wrote it.

I would have Dad evaluated before this GF talks him into getting married. If already evaluated, get a letter from the doctor.

Wouldn’t Dad have to sign? Is she his POA? If he’s been legally declared incompetent his signature is not valid. If she is his POA and you have concern this will happen, I’d have an attorney on board just in case.