"the tarred palings..."See in text("The Doll's House")
A paling is a fence made of pointed stakes of wood or metal. The fences being covered with tar instead of being painted an attractive color suggests that the school is ordinary and does not cater to the children of the upper class.
Since New Zealand, a former British colony and the setting, several words in the text, such as “carter,” reflect English culture and word choice. A “carter” is a person who “carts” or transports goods from one location to another.