That type and color of box was used 1911 to 1919. The text of the label (below) narrows it down to 1911 to 1915.
In 1916, they added the word "incorporated," in small print, under the Rem-UMC line.
REMINGTON ARMS-UNION METALLIC CARTRIDGE CO.
AMMUNITION & FIREARMS
UNION METALLIC CARTRIDGE WORKS
BRIDGEPORT, CONN. U.S.A.