An individual presented a check drawn on our bank for an exchange for cashier's check, however, the teller processing the transaction did not look at stop payments on the account and therefore was unaware that the check being exchanged had a stop payment placed on it earlier the same day. Do we have any recourse or ability to stop payment on the cashier's check?

Not really, but look at the reason the stop payment was placed.

If the customer purchased merchandise and was unhappy with it, you may ask the customer for the merchandise. They are not entitled to the merchandise and their money. Not that you will want the merchandise, but it gives the customer a decision to make and often they choose the merchandise. Doesn't always work but it may be worth a try.