The glass is very similar to the Baccarat
Bamboo Tors pattern as seen in the 1916 catalogue - page 043 has a lidded powder box with a similar metal part... the one illustrated is the Rose teinte version not clear like yours but we do know the pattern was made in clear also, but.... the lid on the Baccarat one appears to be flat not patterned like yours, and the intro page of the catalogue states that each piece carries the
usual Baccarat stamp displayed on the same page (which isn't a B).
Tous les articles de notre fabrication portent une étiquette, une estampille ou un poinçonnage représentant la marque ci-contre.
which Google translate helpfully converts to:
All products in our manufacturing carry a label, a stampille or punching representing the above-against mark.
So I suspect not Baccarat but possibly a lookalike for what was a popular pattern at the time...