I wouldn't worry too much about it... as others have said, just keep it at home and use it there, or return it to a Zeta. (Or be prepared for curiosity from Zetas
)
AEPhi's rule is that only initiated sisters are supposed to wear letters or use anything with letters on it, so if I saw someone with an AEPhi pen I'd assume she's an AEPhi, but I wouldn't be too put out if she weren't. If I saw someone
wearing letters who turned out not to be an AEPhi, then I'd explain the rule and ask that she not wear the letters again. But a pen is just an object...