We have tried both, and what seems to work best is leaving the background in naturally. We see higher CTR and Lead generation and our theory is that people want to see the most up-to-date photo in realtime. It builds more trust with the consumer. When we add the date to the bottom right of the photo, or take the photo out side with our dealerships in seasonal locations, people get the idea that inventory is fresh on the lot and want to be the first to grab it.
If it is hard to get your merchandise photographed consistently or updated, it may be better to remove or replace the background. You don't want snow on the ground when it is summer, or a date displayed that shows the age of the new inventory. On the other hand, If removing/replacing the background isn't done cleanly then it can ruin that first impression. I don't know what takes more time, removing/replacing the background and editing to perfection, or re-shooting the vehicle on a nice day.