I have a pretty good collection of Western Cartridge Co. and UMC and Rem-UMC paper to judge the age of boxes. If the box says Union Metallic Cartridge Co. it is 1910 or earlier. If it says Remington Arms - Union Metallic Cartridge Co. it would be from the 1911 to 1916 time frame.
NITRO CLUB 28-ga 1 3-4 dram, 5-8 ounce.jpg
If the company name is The Remington Arms Union Metallic Cartridge Company Incorporated it is 1916 to 1920.
NITRO CLUB X20D7 Remington Arms - Union Metallic Cartridge Company Incorporated.jpg
In 1920 a new company was formed, Remington Arms Co., Inc. and early boxes like this carry the "Successor to The Remington Arms Union Metallic Cartridge Co., Inc." line.
NITRO CLUB X23-7 1-2 Remington Arms Company, Inc. Successor to The Remington Arms - Union Metall.jpg
Later it was just the Remington Arms Co., Inc.
NITRO CLUB Heavy Duck Load top label.jpeg
Kleanbore priming was introduced in 1931
Arrow Express Lacquered 3-inch 20-gauge 1931 vintage.jpg
and for a couple of years they used green two-piece boxes and then during 1933 they began using the one-piece boxes.