the americans didnt gave greenland back to denmark because of the arctic route to the soviet union
here the nazis woulndt give it to the italians because of bombimg in case of ww3 Malta and africa(Cairo, Lybia, etc)
No, the americans kept greenland because Denmark is allied to the axis, while Italy is allied with Germany so the italians would let the germans keep their airplanes there, there is no reason to keep it occupied