I don't think it's a stencil, why would they need a screw hole through it if it were a stencil?
I'm thinking it's the cover to a ladies or gentleman's Georgian Period Vinaigrette.
"Vinegar was considered an indispensable item in the 18th century for arousing a fainting person or masking foul odors. When the sponge was soaked only in vinegar, its original use, it could help prevent the wearer from fainting. A person stepping outside a crowded London street might carry aromatic soaked sponges to hold close to the nose to mask the odor of raw sewage and rotting garbage. In the early 19th century, there weren’t garbage men that carted away the trash. People threw the stuff out the window. Slop pails went out the window in the 18th century. And when you left your house, you would encounter odors that made you just choke. So, they invented a device called the vinaigrette… a box or a little trinket carried to revive oneself if one felt faint. So now you can’t breathe when you go outside, you smell the rotten garbage and the sewage, and you think they’re going to faint. You would opened up your vinaigrette, which you hold in your hand, and inside is a gold-pierced grill with beautiful decoration. But underneath the grill is a sponge. Ladies would soak that sponge in an aromatic solution, sort of a mixture of perfume and ammonia, like smelling salts."