She called up the salesman who sold us the car and asked ingenuously if we had purchased the warranty. The salesman was very sympathetic, and dug up the information that there'd been a factory problem that year. The end result is that Honda offered to pay for the parts to replace the transmission if we paid for the labor. This was an excellent deal, and we took it happily.
The salesman is Gerry Anderson at Valley Honda. Every time we've dealt with him, he's been so friendly and nice that I keep expecting the other shoe to drop. So far, though, no such shoe has dropped; he's taken good care of us both before and after the sales. (If you buy a car from him and mention my name, I think I might get a small referral bonus. But the bonus certainly does not make it worthwhile for me to lie about how good he's been.)