Never thought of checking Hobby Lobby for leather. Is it any good? I bought a strop from Woodcraft and I wasn't impressed with it. I also bought a sheet of the leather that they sell which is pretty firm and attached that to the other side of their strop and it seems to work better. Wonder if the DLT strops are like that. What really works the best in my opinion is this old leather wallet I had laying around. Its black and soft and I tried stropping on it one day and it gave me an amazingly toothy edge so I sacrificed the wallet and was able to salvage a nice rectangle piece that I glued to a board. After stropping on the other hone I always make a few passes on the wallet and you can feel the results immediately. I have no idea why it works so good and with no compound either. Wish I could find more of it as I'd love to slap some compound on it just to see how it would be. I leave this one natural as I don't want to ruin it and it does such an awesome job. I think its made of out magical unicorn ass

Seriously, its so great. Wish I could send people samples of it.
I've bought some fairly heavy & thick leather 'scraps' from Hobby Lobby, in a 3 lb. bag. Also a couple pieces of what they call 'tooling leather', which is thinner and somewhat smoother. Used with compound, either type can work. But ultimately, thinner and smoother is usually better with strops. I also have one of those leather pieces from Woodcraft. And even though it was pricier (I think ~ $15 or so), I didn't notice any particular advantage in it, over the cheaper 'tooling leather' I got at Hobby Lobby.
I'm guessing your wallet is likely very thin leather, and the preparation of it by the maker might've enhanced it's suitability for stropping (tanning method, pressing, rubbing, polishing, etc). In particular, leather that's been compressed tends to have a higher concentration of natural abrasives (silicates) near the surface, and that will enhance it's usefulness for stropping. Leather is so highly variable in quality, and the price doesn't really guarantee what's best for a strop.
I tend to view a piece of stropping leather that works fine on it's own (without compound) as something of a rare nature. I wouldn't be too quick to add compound to it, as that may defeat any benefit from the leather itself. Used with compound, most any flat & smooth surface can do well (leather or otherwise), so it's kind of a waste to add compound to a truly prime piece of stropping leather anyway. Personally, on my compounded strops, I tend to use other materials (wood, or paper/cardboard over hard backing, like glass) much more often than leather. My 'best' leather strop right now, is the sueded side of a leather belt I purchased from Cabela's; part with green compound, and also a bare section. I use the belt like a hanging strop, and it works better than any other leather (cowhide) strop I've used so far.
I've heard good things about horsehide leather strops, and kangaroo leather, but haven't yet tried them. The more ways I find to get good results with cheaper materials, the less I feel the need to try the pricier horsehide and other exotic leathers.
David