Interestingly enough, when Denmark sold the Virgin Islands to the USA, they obtained the withdrawal of the US claims over Greenland. So today's trumpian claims would contradict a former US engagement (see the link below), unless the USA give back the Virgin Islands to Denmark.
It is true, however, that it wouldn't be the first betrayal from the current US administration ... They obviously don't care about their Nation's faithfulness and interests. I can't see how this kind of behaviour could benefit the USA on the long run. Who would be crazy enough to support a country invading its own allies (apart from its traditional enemies) ?
This wikipedia page alludes to this treaty (see end of chapter "1915–16 negotiations") :
https://en.wikipedia.org/wiki/Treaty_of_the_Danish_West_Indies