Consider this:
I once used an aircraft to do a favour for someone and deliver a passenger for something important. We had a bird-strike when I went for a short fly whilst waiting for the person to do what I took them there to do.
I didn't pay to hire the aircraft as I was doing a favour of the owner of the aircraft. Tricky situation. I didn't hire the aircraft, but I was flying it on a private flight when the damage occurred.
Liken that to your situation and consider that your agreement didn't cover such damage and who might be liable.
Add to this already tricky situation that when the bird-strike damage was repaired, a 6 inch crack was found in the engine block. Ouch. Not my fault, but will the owner of the aircraft agree with you if that happens to their pride and joy???
Whenever I borrow or hire an aircraft I sure as hell always fly the aircraft in the manner demonstrated to me by the owner or competent person, even if I disagree with the operation; eg. use of mixture. It's not my aircraft. If I deviate from their direction given I feel liable if any issues occur regardless of whether it is actually my fault or not.