This is because the ‘s indicates the the noun after it, eyes, belongs to the parents. “parents”, firstly, would indicate that there is more than one parent, which contradicts the information in the question, because it states “parent” instead of “parents”. Secondly, “parents”, by itself, only indicates the presence of the parents, as it is a noun, and does not imply anything about the “eyes” belonging to the parents.
I hope this helped! Have a nice day! 🙂