1st Division Lapel Button, veteran's piece? BB&B

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I just won, on eBay, this piece, a 1st Division lapel button, nicely made and enameled by Bailey, Banks, and Biddle. It is very small; the shield is 7/16" tall by 1/4" wide; the button back is marked "BBB Co./ Phila" and is affixed to the shield. I'm sure I paid too much for this, but I've never seen one like it, and I really wanted it.

My questions are: I assume this is a veteran's piece, but is it from a formal veterans organization?

Does this date from the 1920s-1930s?

Any help would be appreciated.

Thanks,

Pete

(I'm not sure if this is the right place for this question; moderators may move it if necessary.)