If the banks are not doing so, all bank accounts need to be changed. New numbers, etc. Not just the ones she gave them, but EVERYTHING.
In fact, it might not be a bad idea to change banks entirely if that is feasible. If it's not, the savings accounts need to be password protected to prevent electronic withdrawals. Not sure if all banks offer that or not, but it's a feature that saved a friend a LOT of money when someone tried to do an automatic offshore withdrawal using his information. He's still not sure how they got it.
Also suggest new credit cards, and placing fraud alerts on your Mom's credit reports to head off anyone trying to open new credit accounts using her information.
Finally, keep a minimum amount of money in her checking account. Just enough to cover a month's regular bills. Other funds can be transferred in as needed. If someone does manage to burn through the security the loss won't be that bad.
It's likely that they also got your Mom's social security number and her date of birth. I'm not sure what can be done about that, but it's something you need to look into. Same with the DMV if she still has a driver's license.
This is something that I really fear happening with my Mother. I've got daily control of her accounts at the moment, and am paying her bills, but she's getting to the point where she's an odd combination of paranoid and trusting, and you're just never sure what you're going to get at any one moment.