Somewhere I think I've heard a rule about initiating a battle of wits without a proper weapon ...

While perhaps a bit rude, no worse than her instigation.

While matching another's rudeness is not too "civilized," I wouldn't waste lamentations over any possible harm.

The worst that can happen is that at your next chance encounter (which might happen if you both frequent the same bus, or even just the same neighborhood?) she'll have thought of what her reply should have been. (Which is unlikely to be more clever than the beginnings of the tale.)

John