ZTA was one of the first few sororities that I heard about. In fact, when I met a couple of Zetas (plus girls from a couple other chapters) in a class of mine, they made me want to go Greek.
I know that before I joined and shortly after my bid day I was unaware that there were more than 14 NPC organizations. During recruitment, I remember talking to a friend of mine from another school about "a chi o" (this was on AIM so when we talked about it it was lowercased). She said something about how the Make a Wish Foundation is their philanthropy, and I thought that sounded weird because the "a chi os" told me their philanthropy supports victims of domestic violence. I shrugged it off to a difference in local philanthropies. Turns out, she thought I was talking about Chi Omega instead of ALPHA Chi Omega. We don't have Chi O at Maryland (plus at my friend's school they got by Alpha Chi--probably to avoid confusion--and she probably missed the "a" since it was lowercase), and I was unaware that such a grand sorority existed. Also, I remember looking on websites while I was pledging and seeing shirts with Phi Mu or Pi Beta Phi letters and being confused, since we also do not have those orgs at Maryland. However, during my new member period, we learned about Sigma Kappa as a member of the NPC, and that there are 26 NPC sororities altogether. It was an aha moment.
I would be put off too if someone asked me if my sorority was a "real" sorority, particularly because it's NPC and that's what the question connotes. Even if you can't name all 26 NPC sororities and are only familiar with the ones on your campus, the comment would come off as both rude AND stupid/ignorant, because more importantly, both NPC and non-NPC sororities still "real" sororities.
ETA:You mention that your mom and a bunch of other women in your family joined ZTA at the same big southern school. Did you attend school in the South? If yes, I would be extra appalled that the girl at Gingerbread hadn't heard of ZTA, since I think it's big all over the country, but especially big in the South.