Small claims limit in MO is $5,000. Are they demanding more or less than that?
Do you have a copy of this financial institution's contract and terms of service for the transactions? I'm a bit surprised that somewhere in their terms of service there's not language stating that they have the right to withdraw erroneous deposits from your account if they do make a mistake.
When you contacted the financial institution did you use the contact info on the letter, did you use Google to get the company's contact info, or did you get it from an old statement from when you used their services?
Did the letter refer to a specific account number, transaction date, amount, etc.?
How do they want to get paid?

