I wrote "He cleans his bedroom window" but it was marked as incorrect. Is that too specific a room? Since the room is his or hers, I thought it was implied that it was the bedroom.
Bedrooms are the rooms in a house usually designated by individual possession so it's a likely response.
"He / She cleans the window to his / her room." "To" is employable here because it denotes the specific location of the window. Example: The key to his door.