No. You have no way of knowing if the funds belong to the joint owner. The moment the joint owner died, the account became an individual account in the name of the survivor, whether you have updated your system to remove the decedent's name or not.
Any creditor with a claim against the estate could sue the bank for conversion if you allowed these items to be deposited into this account. The checks are not payable to the joint owner and they have no more right to the proceeds than if you allowed checks payable to Brian Crow to be deposited into John Burnett's account.