Greenland isn't a country. It's an autonomous crown dependency of the Kingdom of Denmark.
A much fairer comparison would be asking Canadians what they know about any of the Scandinavian countries (Norway, Denmark, or Sweden). They're culturally and politically similar to Canada in many respects, with a comparable standard of living.
And while it's unfair to expect Americans to know minute details about Canada, we share so many economic, cultural, political, and sporting ties that they should know a reasonable amount just by virtue of proxy. You're talking about a country with a higher standard of living, upon whom many Americans are dependent for their livelihoods, and who exports plenty of human talent to them that play a major role in their film and sports industry (for a couple of examples).
We also share long-standing, very close geopolitical and security ties through our militaries, border services, and intelligence agencies. They should know something.