Problem being that the wording wasn't loose at least in the USA interpretation. The US would of course stick to the treaty being contracted between the legal representative of the Danish government and the USA government. Problem is of course that the new Danish government would object to this as the former goverment was in the pocket of the Nazi's thus no government existed post April 9, 1940 till this communist governments entering into existence.
Then they would probably play into the hands of the USA just by this claim leaving Kauffmann as THE legal representative of Denmark at the time being thus making the treaty valid; at least I would claim so appearing in the Hague if it was taken there.
Of course claiming the political system of the host country being a potential threat to the USA thus allowing the maintaining of US bases in Greenland according to treaty would somehow require Kauffmann being recognized by the USA as THE Danish government in exile following the communist take over in Denmark! (Phew! guess were are closing in on a USA annexation of Greenland in the guise of exile Danish government!)
The latter could prove complicated if the Danish communist government had been legally elected by ballot making any claims to validity of the Kauffmann actions void so the USA may simply decide to A) annexation or B) recognition of Danish government in return of basing rights in Greenland.
As A) would be in violation of US attempts at decolonization efforts B) could become the way to go. (remember this is 1945 pre-Churchill Fulton speech and Truman doctrine)
Its just all conjecture.
As to the second part - how is Danish control of Greenland ex-US bases a threat to said latter? Denmark had severe problems agreeing to occupy parts of Schleswig-Holstein as Christmas Møller had promised the British. It would need a great infusion of Soviet war materiel to move any troops anywhere! I don't really see this as a problem for some time to come. At least not in a 1945 perspective.
Remember the Soviets had problems of their own with famine on the doorstep and need to feed the East Europeans post war.
With a possible German last stand in Denmark resulting in utter devastation due to Soviet military doctrine and execution of operation count Denmark into that sphere needing feeding!