Answer: the key possession is the symbol of power and Nora was not allowed to have that power in the house.
Nora have always hide her crimes and she would not have want her daughter to catch her prying the letterbox.
Explanation:
The key to the letterbox is symbol of power in the Helmer household. Torvald is in possession of the key and is the only person that can access the letterbox. He is in control of the Helmer household metaphorically.
