The short answer is that since the parcel is marked delivered, you are not responsible.
However, as a good seller, follow aubreyclay's advice and try to help your unhappy customer find a resolution on his own. At the very least, the customer should visit the Postmaster at the local Post Office (not postal outlet) and discuss the problem.
The PM needs to know if there have been problems on a route. This may be the fault of the postie (or a temp over the holidays rush) or there may be a theft problem. The PM is the place for the customer (not you) to start.