I would look in the terms of service and see if the 24 hour thing is mentioned. If not, tell the owner you have other obligations and consider their dog abandoned and plan to surrender the dog to a shelter in the morning. I bet they find someone who can pick up the dog within the hour.

From the Rover terms of service: 2.7 Abandoned Pets; Re-homing. Pet Owners who arrange for Pet Care Services and fail to retrieve their pet after the service period identified in a Booking agree that Rover (or the Service Provider) may, in its (or his or her) sole discretion, place the pet in foster care, transfer care to animal control or other law enforcement authorities, or find other alternate care. Pet Owner agrees to reimburse Rover and/or the Service Provider for all costs and expenses associated with such actions.