Apart from the wording of the OP, I can basically understand well that he doesn’t like it. A large tree probably won't grow on the narrow strip. But the parking space should of course still be usable. Leaves are less of a bother, but bird droppings would really be annoying. Especially if the car is left unattended there for a longer time, which should basically be possible for a parking space on a private property.
I would try to find out what kind of planting is planned there. However, remain friendly and do not refer to "baumwichse." I wouldn’t mention the fear of leaves on the car either, because that makes you look ridiculous. Chestnuts, resin, or bird droppings would be the reasons for me to oppose a certain type of planting.