I'm curious how he told you this problem? In writing?
I have banked a few deaf clients. They communicated via sign if we had someone to do so, or in writing. The act does not require that we train everyone who might come in contact with someone who is deaf on sign language.
Now on the other side...I learned so I could deal with this client in a more effective manner (they were a regular with enough needs that this was valuable). I wouldn't have done it because they required me to do so, I did it because I liked this client a lot and wanted to be more helpful than I could be in writing back and forth.
You could ask this client if they read lips and then speak to your staff about talking with the deaf. Many people don't think and talk without looking at who they're talking to. Perhaps they turn around and grab some change while continuing talking. This would make it impossible for someone who was deaf to understand what was being said. Some sensativity training would go miles if this is the case.
Our client noticed it, yours might as well, but no need to institute training tomorrow