But the US could just leave. No need to have a costly war over it. And why Greenland, when invading Canada is probably easier?
Or just do nothing. Silently decide to not support other countries when they get attacked. But keep on using the joint radar bases in the north and the logistical hubs in central Europe.
This being a distraction and/or Trump the Conqueror wishing to turn more regions on the map US colored seems most likely to me.