I think for future sits, I would plant the thought and see how they respond as - chances are - they just havent thought through the implications for you.
They indicate that you need to drive their dog for its walks. And then you ask, “OK, will you be able to leave me some cash to cover the fuel? Do you have covers for my back seat? How does Fido travel, is he good in the car, does he have a doggy seatbelt for me to use?”
(Disclaimer, I had no idea that dogs-in-sitters’-cars was such a hot topic until I joined this forum. They may be as clueless as me and just need a nudge 
)