Possibly could be one of them wick raiser knobs from an old kerosene lantern, seems like the right size and has the mark in the very center. Just a guess though
Without knowing the exact size, I'm thinking Tack Driver nailed it... I mean 'thumb wheeled' it.
The 'Star' branded burners were produced by H.B. & H. (Holmes, Booth & Haydens) in the 1860s - 70s.