It's the optional unspecific subject. One of the its functions here is to indicate that 'groene kaas' is the object of the sentence... otherwise, the same question could also be interpreted as 'Who(m) had green cheese eaten' with 'green cheese' as the subject. Having 'er' removes this ambiguity.
When you are in Friesland you will find packings with griene tsiis, since we are proud of our language. In other parts of the Netherlands people won't understand you. The words skûtsjesylen and fierljeppen are the only Friesian words I can think of which are also common used in Dutch
True, it's not as universal as I mentioned in my previous post, I'll adjust it. However talking about how these sentences are used in practice I think there is a clear difference in the importance of the location of cheese that was eaten and a house that was built.
The amount of situations where the cheese sentence could/will be used is vast and right now I can't think of any situation where one would keep on using er instead of hier or daar if the location is important. So I think it makes sense to not accept there. (Keep in mind that the goal of Duolingo is to teach people a language they can use, not to teach unusual sentences that only work theoretically.)
For the house example that's clearly different, and there should be an accepted answer.