Remington, as far as I know, didn't push a club of its own during those years. Its advertising took a different tack as well.
"War Department Offers Rifle Shooting Medals to Boys," from a 1917 issue of the Saturday Evening Post, is an example of Remington's approach. It used the lure of government-sanctioned marksmanship awards, along with the credibility of the Boy Scouts and the NRA, essentially to soft-pedal the brand. An excerpt from the copy:
"Another thing -- you don't have to shoot any special make of rifle and ammunition to compete for these National Medals. You can use any make of .22 caliber rifle and .22 short cartridges.Two years later the W.J.R.C. was on the scene. Remington adjusted its pitch accordingly.
"We hope, of course, that you will select Remington UMC. Certainly you will, if you ask advice from men who know."
"News Indeed for the Young Man and his .22" popped up in a 1919 issue of Collier's. The ad's subhead -- "Individual Shooters Recognized by N.R.A. -- No need to join a Club" -- was an appeal to youthful independence and a shot across Winchester's bow. Later, this:
"Now don't hesitate to write us just because your rifle or ammunition is not Remington UMC. You don't even have to tell us what make you do shoot -- now. We'll take a chance that you will come to Remington UMC as your skill develops and you become more critical about your arms and ammunition."And so the two companies exchanged volleys, vying for young shooters, their skirmish lasting nearly a decade. Which one prevailed?
Remington is still around -- it's the oldest company in the U.S. still making its original product, the oldest continuously operating manufacturer on the continent, the only American company that makes both guns and ammo here in the U.S. and the largest domestic manufacturer of long guns.
Winchester, which always struggled, sadly (or mercifully) is gone.
The W.J.R.C. had a successful nine-year run before it was absorbed by the NRA. Its descendant, the NRA Marksmanship Qualification Program, continues to thrive.