Not sure why you had to pay to get it out of the yard if it is yours and was stolen then recovered.
Someone has to pay for the services provided by the tow company, the police cannot leave the vehicle once they recover it so they must remove it from the location for safe-keeping. The vehicle is your responsibility so you must pay for the expense to move it. Something your insurance would pay for if you had full coverage. If they ever catch the idiot that took it you could sue them in small-claims but I don't see that happening.
