I felt sorry for the rat after reading the title. Then I realized he was damaging the plaster/sheetrock. Anything that causes me to get out the spackle or a paint brush is gonna make me livid. I once duct-taped the two-year old grandchild to a stair post all day because she drew on my wall. Rat deserved everything he got.
How did the mouse get into the 4x4 box? Usually not much room in there, or a way to access it.
Solution to two year old drawing on the wall is to tape some butcher paper to the wall and tell her to stay on the paper \.