When discussing the application question that inquires about your parents’ college background, the word “valid” isn’t … well … valid. 😉 That is, there is no “good” or “bad” way to respond to this question, and your admission decisions won’t be linked to the prestige of your parents’ alma maters.
I imagine that some admission officials will recognize the names of the Korean universities that your parents attended and others won’t. But it doesn’t matter. The primary purpose of this often-controversial question is to allow admission officials to ferret out the “first-generation-to-college” candidates who commonly get a small advantage in the admission process and are sometimes eligible for special scholarships. When admission officers see that an applicant’s parents did attend college, it doesn’t matter so much which college they attended; it simply tells them that the applicant is not “first-gen.”