ABSOLUTELY 4J! You hit the nail on the head! Put a stop to the drafts from the company you have no idea who they are!
Simple enough, leave enough money in that old/original account to cover any checks or debits you have made, plus a little, put the rest of your funds into a new account at a different bank. Very little hassle for the money you will end up keeping.....no waiting for that 'company' to quit taking funds.
Make sure your 'old' Bank understands-in writing-that they are no longer authorized to pay out to that one 'draft'.
Make sure once you have the new account at a different Bank that you can set up a new Draft account for the mortgage payment if you wish.
Cancel the old Draft at the old Bank for that Mortgage and make sure everyone is clear-IN WRITING!