Thats a robin not a woodpecker =)
I don't know what to say (Shoot the bloody bird and bury it in the backyard or something) I don't know what else you could do other than not polishing your car, the birds are attracted to their reflection and think it's a competitor so tries to peck at it. I have seen birds kill themselves trying to peck at their reflection. So if you can get the car in full shade to cut down the reflection that should help.