All I could find is T W & W stand for Trelon, Weil & Weil. A company from Paris and strictly made buttons in the mid 19th century to possibly early 20th century. Look up the company and see if you can get any better ideas on the age and type of button!
Depose in this context just means registered/patented basically.
Edit: I realize Brevete, also often seen, is really the more accurate for patent, but I just mean that these terms are not company specific.