Damage to my car and refusal to pay because i cannot prove they damaged it

I took my car in because it had a steering lock problem. Upon repairs they broke my gear lever selector cover. It does not clip back on so i have all the wires and components exposed. TI showed them this right before leaving on the day i collected my car( 10th of Oct 2023). They promised to replace it for me, they looked for a second hand and unfortunately they could not find one. So the only other option was to order it from VW directly. After they realized that the cost of that cover is more than what i paid in cash for the repairs the were doing initially, the workshop manager told me that his bosses said they WILL NOT PAY FOR THE GEAR LEVER COVER solely because i cannot prove that it was not broken when i brought the car in and also i cannot prove that they broke it.