Dealership sent an invoice for a machine they contaminated using my car

r/

Location: Ontario, Canada. I took my car in to a dealership shop to get its AC looked at since it’s covered under warranty (separate warranty from the dealership it is being fixed at, the one I bought the car from doesn’t fix cars) and they told me that it’s a refrigerant leak and they’re going to replace the refrigerant with dyed refrigerant to track the leak. Anyways so I get the cost approved by the warranty team and tell the shop to go ahead with the repair. Turns out my car had the wrong refrigerant in it and now the shop is sending me the invoice for the cost to decontaminate their machine and tank they sucked it out with. Is this really my fault since it was my car that had the wrong refrigerant, or is it the dealer or the shops fault?

Thanks guys.