Denmark is largely beholden to the United States in many ways, but their biggest contribution was the asylum of Niels Bohr in the US during the Second World War. He was President of the Royal Danish Academy of Sciences, of the Danish Cancer Committee, and Chairman of the Danish Atomic Energy Commission, among his contributions in life. Dr. Bohr was spirited out of Denmark shortly after the occupation of Denmark by the Third Reich, as he was of Jewish descent, and would have ended up in a slave labor camp or even liquidated during the Holocaust.
His theoretical studies led to breakthrough discoveries in the development of quantum physics, and made the harnessing of atomic energy possible, first as a nuclear weapon, then later in the development of nuclear power generation. Dr. Bohr began his work on the Manhattan Project after fleeing to Sweden from Denmark because of German occupation. So in a way, there has been great interdependence with historic ties between Denmark and the United States.
Tha sounds like the US owes Denmark, not the other way around.