Keep it as long as you want or until you see an opportunity to give it away to another family member (someone looking for a car to restore, you'd be the favorite uncle/cousin), besides, it's paid for. In the mean time, enjoy it and maintain it as well as you can. Please, don't give their money back at any rate, it's a token or a gesture; the car could become something of a memento.
Come on, Clay, snap to it! This is a generous, family-based, likely one-in-a-million offer. Now, give the Lincoln a rather endearing name with a reference to your Dad and brother.