If Oyster had been used for London Underground
only, it would not be one journey. However, as the Oyster part of the journey contained at least one NR leg, so the Oyster leg is subject to the
Oyster Conditions of use on National Rail services which says
(Yes, it hasn't been updated to refer to the new NRCoT, but I am going to consult the NRCoT as its accepted that it supercedes the NRCoC)
So, Chiltern won't refund any extra that is charged to your Oyster because of delays (presumably because you can usually already get this refunded by calling the Oyster helpline anyway). Delay Repay is a separate concept though, and Oyster travel
can qualify for Delay Repay.
We all know one way the NRCoT allows multiple tickets to be used for one journey:
However, neither NRCoT 33.1 nor Chiltern's Passenger Charter doesn't explicitly mention what happens when multiple tickets are used, so it may be difficult to get them to pay Delay Repay based on both tickets.