Given the period discussed, that would make this into the modern era if a pipe cover. Tobacco was a relatively late addition in Europe. Or maybe they smoked other things? I
still think candle snuffer, even a basic one used in a
church with the crosses. I have seen candle snuffers this small or smaller. I have seen them on long sticks, as well as handheld. But, if
attribution is much later than
Roman, pipe cover also makes sense. Interesting little piece.
Virgil