Translation:The restaurant is dirty, but the food itself is not bad.
As you know, Duolingo prefers noncreative answers (those that don't exactly follow the wording of the lesson). The developers can't possibly think of every iteration of meaning. But in reality, your sentence is correct, because "per se" actually means "in itself." And this is what "yemeğin kendisi" means: "the food itself" = "the food per se."
I would say it has a slightly different meaning - putting per se there puts emphasis on the "bad", so you're saying the food wasn't quite bad, but it was something almost bad. Whereas this sentence is saying that the food is fine; the cleanliness problem does not affect the food.
Yes, "yemeğin" can mean "your food" ...but in this case, it's a 2nd person (sen form) possessive suffix, not genitive case ending :-)
In this sentence, "yemeğin kendisi" is saying "the food's self = the food itself". So yemeğin (in this context) is using genitive case to mean "the food's /of the food". And the possessive suffix (3rd person singular) is on "kendisi". :-)
I'll link you back to the Possessives /Genitives Tips and Notes if you (or anyone else) want to review :-)