As bad as it sounds I shoot them. Its 4 months after Xmas and time for people to start dumpin dogs on dirt roads. Easter dumps start in late august, usually more cats than dogs.
So sad but thats how it works.
I encounter the same, I've even had them drive by with the dog in the bed of the truck while we're outside, drive back by about ten minutes later, drive 100y down the road from the house, kick the dog out and take off.