Modern Steel Equipment Co., Geneva, Ill., had four contracts for ammunition boxes (1 specified "AMMUNITION BOXES" 1 specified "AMMUNITION BOXES CAL50" and 2 specified "AMM BOXES CAL50 M2") that ran from October 1942 to December 1945 for a total of $4.8 million. Obviously they made allot of ammunition boxes, including (probably) your example.
I don't have the resources at hand to research the ordnance plant with intials "TW" and the years of operation, which may yield another clue as to the approximate year your ammunition box was manufactured. Information on the lot number and ammunition type may also provide year of manufacture. If you have any of the cartridges from the box they will of course have the year of manufacture in the headstamp.