Polydactyl cats and "mittens"

In one place, the recent mailbag article seemd to imply that double-pawed cats are also called “mitten footed cats”. (I couldn’t tell for sure from the wording; perhaps “mitten footed cats” referred to a different kind of cat entirely which may have originated in New England.)

Anyway … does this mean that cats with extra toes (or complete extra paws) are in some way related to the nursery rhyme about “two little kittens who’ve lost their mittens”? Does the “lost their mittens” part refer, perhaps, to polydactyl kittycat amputation?