Here's the good news: you can still do the quest with the glove on the table!
The glove is actually not related to your progress on the quests. As in, even once you've finished all the quests, the glove will still be there. It's just a decoration supposed to show you that it is "THE" worktable.
So just ignore that glove, and continue on as normal, and you'll be good!
May Aether always be in your Aethermeter,