Tedd's Glove is glove Tedd is using to program magic watches. Tedd never explains it, so we can only speculate about it's functionality. It is certainly different object than Tedd's Gauntlet (not only it looks different, we have confirmed it by Dan), but it may still have similar functionality of storing magic energy - or it may be more complicated magic device. It doesn't seem to need connection to computer to be used, although it may be connected wirelessly.
We first see the glove when Grace leaves to secretly meet Adrian Raven in Death Sentence (story line). After that, we are supposed to first see the glove when Tedd prepares watches with cat form for Sarah. We first see it to program watches when Tedd prepares non-furry cat form.