Erving (and anybody here who doesn't already know), the Jim Byce Backmarks webpage is notoriously inaccurate. I urge you not to trust it, nor recommend it. That particular backmark, which says CO'S (the abbreviation for the plural Companies), dates from 1943 to 2000. The Waterbury Button Company website's "Company History" says the Waterbury Button Company changed its name to Companies (plural) during World War Two, and changed it back to Company (singular) in 2000.
Its worth spending $25 to get the best book on button backmark dating, "American Military Button Makers And Dealers; Their Backmarks & Dates" by William F. McGuinn & Bruce S. Bazelon. It is available online from various civil war relic websites. Don't pay more than $30 for it. Also, be sure you're getting the newest edition which has a butternut colored linen cover. (Older editions have a blue, red, or green cover.)