The EU? Not a lot. It's not a member. Denmark? An annual subsidy. Healthcare, social security, that kind of shit.
This is not to say that Denmark does not have a shameful, racist record in Greenland. Like Canada, Australia, and other countries, it has a vile record of horrific practices such as forced adoptions dating back as recently as the 1970s. But that has changed for the better in recent decades and Greenland now has far greater autonomy.
The question here would be how much real autonomy a nominally 'Independent' Greenland would have. Quite possibly less than it has currently given the USA's ambitions. You can bet your arse that the US would invent an excuse to step in and save Greenlanders from ... imagined threat.