hard to admit, but you'll have to take it up the arse and get soem new rubber on it
if there is some cctv about the place then that might do something, but even if they found the person responsible they won't be paying for your tyres
the garage shouldn't be getting your business if thats the way they have responded though, so this "garanteed" pass with no questioned asked might give you a bit of leverage if they tell you to fuck off and don't give you the ticket even with 4 shonked tyres