I too am picky picky. I wrote "The Athen's marathon" and was told I had a typo. I suggest that the apostrophe is required, and Duolingo's answer, which has no apostrophe, has a typo! Είμαι επιλεκτικός. (OK. I looked επιλεκτικός up in the dictionary. It is most probably totally the wrong word.)
I suggest that the apostrophe is required
The city is called "Athens" and not "Athen", so "Athen's" makes no sense.
Also, if you did use 's to form the possessive, you wouldn't use "the" -- for example, you can talk about "Paul's book" but not about "the Paul's book".
But "the Athens marathon" simply puts two nouns next to each other in order for one to modify the other, as with "cigarette lighter" or "Eiffel tower".