Hmmmmm this is wierd. But dumber things have happened I guess.
First things first, I'd not ask, but TELL my other half to call his ex and nicely request the money back. You said they broke up amicably and they haven't been in touch with each other since then so where's the harm? Honestly, if an ex of mine called me to tell me what happened, I'd laugh about it, have a nice catching-up chat, then write a check for the amount he paid and be done with it.
If the other half didn't want to do that because he doesn't like confrontation (again, you said it was amicable so why does he think there'd be confrontation to begin with is beyond me), then I'd tell him to get a spine and grow up, then I'd get her #, pick up the phone, nicely introduce myself and nicely ask for the money back. If she refused, I'd chalk it up to a loss AND my other half's stupidity. And then I'd ask him if it was so amicable, why does she refuse to give us the $$ back.
And in the end, I'd wonder why he still has her info connected to his account and make the changes necessary to keep it from happening again.
ETA: Wanted to mention that the third scenario is that if he refused to rectify this himself by calling her, AND if he refused to give me her # or contact info to settle this myself, there would be serious hell to pay and I'd question his motives and confront the crap out of him.
Oh, and if the situation is legit and your husband goofed, it's not his ex's fault so there's no need to feel any animosity towards her, so why the name calling? If anyone deserves to be called something, it aint her.