C-I-L is Canadian Industries Limited, which operated the Dominion Cartridge Company for many years. They were in the ammunition business, so they liked to support the shooting sports and this is one of the many ways they did it.
There are also similar badges with a big DM on them for Dominion Marksmen.
They were issued in several disciplines, various positions and took in almost the entire discipline of Marksmanship. There were awards for Pistol in CF and RF both, Olympic style and Freehand style. The same thing pertained to Rifle. Shotgun had two main categories: Trap and Skeet.
You signed your piece of paper and you were enrolled. You shot targets which they provided, using (hopefully) their ammunition (although Eley, Tenex and even RWS are known to have crept in accidentally). Your local club looked after your scores and, when you had completed a course, you got your badges.
But sometimes that didn't work. I shot the Indoor Rifle course and qualified for the full SET of pins for shooting Prone 3 times (twice with a Number 7, the final time with a DSM-34) and never did see a pin. As it has been over 50 years, I am beginning to think the Post Office might have lost the letter!
Pins were available in Bronze (which is what this one is), Silver and Gold, depending on your scores. Once you had qualified for your Pins, you then started shooting for the various Patches for your shooting jacket.
It was all very friendly and all very gentlemanly and it was open to any shooter, male, female, young, middling or ancient. They were a simple little reward but they kept your interest up...... and a shooting jacket half-covered with the things meant that you were up against one of the Best.
Frankly, I have NO idea why someone is not doing exactly the same thing today. It kept people out on the ranges..... and the Lord Himself only knows how many hydro-pole insulators these little rewards saved!
So now you know.