usecase - banking

The following story seemed to provide an excellent usecase.

"Help please.....Earlier this year I tried to pay one of my team and
somehow paid some random stranger who is logged in our internet banking
system. (Apparently it's a common mistake with fingers slipping on the
mouse, but we don't seem to have a named recipient for the acc!)
When I realised the mistake, I called the bank and they said the only way
to retrieve the money (which coincidentally is at their branch and they
know who the person is), is for them to send letters to the account holder
and to appeal to their sense of ethics and ask them to return it. My bank
has apparently sent their other client 2 letters which have been ignored
and now they are washing their hands of it. They suggest to me that I
contact the account holder directly. The bank will not tell me who it is
for privacy reasons.

Can anyone tell me how I can sort this out? It's a thousand dollars, it's
not like I'm not fussing over petty cash."