I had a check that I wrote to a store that was returned for NSf. The company submitted the check electronically and it cleared the second time. However, the company charged me a $20 fee for the returned check and this hit my account via a check from the company that listed "verbally agreed to by account holder" in the signature line. Can the company legally do this is I did not authorize that check to go through my account?

This depends on state law. In Wisconsin if there is notice at the point of sale that this is the way it will be handled, it's legal.

Under ACH (automated clearing house) rules, when an electronically processed check is nsf, the nsf fee itself may be collected via electronic check.

Many large companies that process large volumes of checks (the power company, phone company, etc) will have disclosed this in a mailing to its customers.

If the check was given to a merchant (Wal-Mart, the local gas station or toy store, etc.), the notice that the merchant may collect an nsf fee in this manner should be posted at the register. If the notice is posted, and you still choose to pay by check - there's the agreement.