You have two roles here. The first is how to handle the complaint from the customer. Secondly you must decide on the customer relations position you want for the company.
The major issue here is the customer needs a part that was supposed to be finished last week. Today, Thursday, the customer does not have their part. The part we made does not meet their requirements and it would be costly for us to run the part again. It is important to resolve this customer's problem quickly to support our ongoing relationship for future business. I would call the customer personally and apologize for the delay and confusion about the customer's order. I would then explain the situation as we received the customer's product specifications after production had begun. After explaining the situation to the customer, we would then work to resolve the current issue. Although the customer may have to wait some additional time for is part the company would be willing to remake the part at our expense.