Button appears to be have been made by Bastian Brothers of Rochester, NY. I contacted them but their records were destroyed and they weren't of any help.
Any help would be greatly appreciated.
The eagle and red, white and blue made me instantly think veteran also. The American Legion was founded in 1919 in France. There might have been other attempts to form veteran organizations at the same time. The thing about organizations that are specific to a given war, like the GAR, the members all pass on and the organization ceases to exist, except there are now sons of the GAR, but you know what I mean, the actual veterans are gone, while the American Legion and the VFW aren't specific to a given war for membership. I counted 103 currant American veteran organizations, and the WWVC wasn't included, so I'm thinking the organization has been out of existence for some time, or at least Google doesn't know anything about it.