The pug gained particular significance in Europe following the bill issued by Pope Clement XII in 1738 forbidding Roman Catholics from belonging to Masonic orders. Many high-born Catholics formed themselves into quasi-masonic lodges and took as their symbol the pug-dog. These Orders of Möpsen (after the German for "pug") were pledged to secrecy, though not by an oath which would have conflicted with papal wishes.
Unlike Freemasons, women were admitted to these lodges. The ownership of such a box might have replaced the model pug which all initiates carried during lodge meetings.
For more information on this subject, see A. Somers Cocks and Ch. Truman, The Thyssen-Bornemisza Collection - Renaissance jewels, gold boxes and objets de vertu, London, 1984, pp. 270-271.