It also is not even clear to me that the Pearstone people know what "transformer" means. It seems likely that their copy-writers grew up thinking that "transformers" were some magical mechanical creations that could turn a semi-truck into a 100 foot tall robot monster. Or maybe they think that "transformer" means some cable that "transforms" one connector type into a different one (i.e. what we used to call "adapters")
I thought a transformer was the thing in my neighborhood that explodes every time a squirrel jumps on it...
Honestly, though, I'm with Richard in that the cable is the likely culprit... but I would love to know if the mic sounds better through an XLR-capable device.
If you don't trust your own skills to examine and rewire the XLR connector as Richard suggests, you might call a company like Markertek that is staffed with folks who make custom cables and know what they're doing when they do. Otherwise, get a box. It's going to cost more than the cable, but it's going to save you some headaches.