I’d still probably go with re-homed for that. Rescue to me definitely implies doing a bit more.

I know someone who drove to a dodgy area to collect a dog which was being starved in a backyard because it’s owner was in prison, and I’d definitely say by doing that she rescued the dog. Other times the pet may have been rescued, like a chicken that was retrieved from a tree in Chinatown by the fire brigade. In which case it is reasonable to refer to them as a rescue chicken, but that doesn’t mean the person who then gives them a home should get credit for the rescue, they have still just re-housed a rescued animal.