Tedd's Glove is a glove which Tedd uses to program magic watches. Tedd never explains it, so we can only speculate about its functionality. It is certainly a different object from Tedd's Gauntlet (not only does it look different, but we have confirmed it by Dan in commentary)[1], but it may still have similar functionality of storing magical energy - or it may be a more complicated magic device. It doesn't seem to need a connection to computer to be used, although it may simply connect wirelessly.
Usage
We first see the glove when Grace leaves to secretly meet Adrian Raven in Death Sentence 4.[2] After that, we are supposed to first see the glove when Tedd prepares watches with cat form for Sarah.[3] We first see it to program watches when Tedd prepares non-furry cat form.[1]