Had the same thing with our next door neighbour, again did not relizied it was here until we spotted it happening.
Again, elderly and she did not know she was marking the car, she used to swing out the door of her car as far as it could go, then lever herself out using the door, which left little vertical scratches to our car.
TBH I did not mention it to her, she was a great neighbour and had enough on her plate to contended with.
MF – Could your neighbour park his car the other way round so his door does not open onto your car, or is there scope to jiggle the space so it makes it easier for both of you?