This thimblything (pictured left) is a Dentipet Finger Brush. One brushes one's pet's teeth with it. I do not have a kitty, but I think every office/breakroom in America has had one of those "How to give a cat a pill" essays posted somewhere in it, and this brushing-one's cat's-teeth thimblythingy reminds me of it. Dangerous business, I would imagine. This one is available from The Vet Shed.
It looks suspiciously similar to the baby finger-tooth-brushes (pictured right) found on another website.