if your child breaks vase at friends house even accidently you should offer and be willing to pay, they may refuse but you should be willing to repair any damage your child does
you do not have a licence to damage other peoples stuff just because it is not where it ougt to be, if next doors kids kick ball into your garden if it breaks greenhouse window they or their parents pay for it, if it just lands on grass you can not puncture it just because it landed on your lawn
i think you have to pay, a car is quite big if your son can not avoid big objects he is not safe to cycle on pavements either, he could have bumped into frail old lady, a pushchair or lamp-post
it is not always illegal to park on pavements it is illegal to block pavement should be room for wheelchair, pushchair, person with guide dog etc
reasonable payment would be t cut or one of those pens that fill in scratches however if scratch is down to base metal it will need re-spray, technically i think you would be liable if someone did bother with small claims court, that would be OTT
personally I would go round and apologise and offer to cover costs, I alos think your son needs to realise that even accidents cost money to put right