Greenland is part of the Kingdom of Denmark, but it's not part of the EU. It was originally part of the EU (back when it was the EEC) but voted to leave in a referendum in 1982, officially exiting in 1985. Today, Greenland has a special status called Overseas Country and Territory (OCT), meaning it has trade deals with the EU, but EU rules don't directly apply there.

The threat is something Denmark will have to respond to in some way. The rest of this is specious.