Crew timeout caused an IRROP where flight was pushed to the next day. No alternate flights as an option to get me home. I'm GM and was offered hotel and food voucher. Was in the lounge and declined food voucher but accepted hotel. Then I found a way to get closer to destination but not the same airport (same original date). Now need to either rent a car or get a car service or taxi etc.

Delta advise hotel voucher disappears, I am fine with that,, but is it worth writing to ask if they'll cover cost of car home? It's cheaper than the hotel which now they don't have to cover. Or is this just doing them a favor?