You may have seen the silicone sleeves they sell expressly for peeling garlic. They work really well, but I can't commit to purchasing something like that. But then! Then I realized I own a silicone baking mat! Suppose you were to roll up the garlic inside it? Would it work?
Lay some garlic cloves out on the edge and roll them up tightly. Roll back and forth - the silicone "grips" the peel and takes it off easily. I was pretty thrilled to discover a second use for my baking mat.
Of course, you might not own a silpat, in which case, too bad. You ought to get one. Save on parchment paper.