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Firing on one British officer would be as bad a firing on 10000.
It's about lines.
But the sun would rise the next day and the USA won't like the 'non-kinetic' consequences. Too many to enumerate.
Eventually the adults in USA would just return it.
It's not an exercise we should entertain, though the EU needs to step up in a very serious way and spend billions of Euros adding new equipment to Greenland to beef up detection and defense.
Most regular equipment doesn't work in -40C temperatures, to take Greenland USA would need to develop more arctic enabled weaponry just for that.
The US literally has bases in Alaska and Greenland and deals with these temperatures regularly.