It's an interesting word, mitt. Not the derivation, so much, which quite quickly runs into the sand (see below), nor its use as a short form of the word mitten.
(Still, while I'm here, there are, of course, oven mitts:
photo by Lymantria
and baseball mitts:
and mitt is also a slang word for a boxing glove.)
No, to me the interesting mitt is the one which means a hand that causes mess, inconvenience, and possibly crime.
Here, get your grubby mitts off that clean washing!
(Though grubby mitts aren't necessarily actually grubby. They might just be naughty, as in: keep your grubby mitts away from that cake!)
Someone with a history of petty theft might have mitts: lock the drinks cupboard, Bob, or Uncle Bernard'll have his mitts on the ginger wine.
Mitt's meaning can be extended into metaphor, too: that scheme's got her mitts all over it. (That is, it shows signs of her self-interest.)
So: where can you spot your nearest mitt? In a kitchen, or on a sports field?
Or sprouting from your wrists?
If not, then whose hands do cause mess, inconvenience and crime?
It's not that difficult, is it?
painting by Paul-Charles Chocarne-Moreau
Spot the Frippet: mitt. This word is short for mitten, which comes from the Old French mitaine.