Ok now I see how they might have been slipping it through,you put together wrap pads in advance,it goes in to your wraps,but you usually want them pre-done because your running on the clock,and theyre pretty easy to screw up if you let your mind wander,so youve allready got them pre-done in your wrap kit if your working a corner. They really dont get checked much,because if they get prodded and poked too much,the whole thing falls apart. It being in the wrap cushions makes sense, that would be just about the best place to stash it. The gloves are supplied by the promoter, most of the wrap is done in public,but the wrap pads are usually done in advance of the fight,and are just sitting in the cornermans kit.
To explain a wrapped cushion of guaze is put right over a fighters knuckles,basically an extended oval of gauze,it looks like a gauze pickle. Those are usually pre-made in advance,so you can just tape them down real quick. But if you poke and prod the hell out of them,they start to unravel.