Don't know if what we see is something different but we see some mesh pads actually etching floors either wood or stone. Some of the products sold at the big box stores have an oilish substance. If you look at the packaging you can actually see an oily residue on the clear bag/package.
I'd assume it's similar, Ron. Not only an oil residue, but the actual product is made from oil(rubber, latex, etc.) sitting under a rug on top of polyurethane.
The sticky white checker board style of mat is the worst. You put it under a rug next to a sliding glass door that gets sunshine(heating and cooling daily)... Your screwed in about six months! People also like to use rugs with latex(wont slip) next to doors, also very bad for wood floors.
Bad for carpet also, the floors need to breath, ever seen white carpet under a rubber mat next to a glass door, it's yellow.
This is the type of advice I try to give every client, you think some 22 yr old working for beer money knows this shat? Every client with wood, as she/he is getting invoice ask them what they are using to clean their floors. Pick a product and recommend it. I recommend Bona for wood to clients, it's just about impossible for them to screw it up. Give them advice about mats and your a guru!
Nice rug.... Lol! Basically that STUPID rug just cost them thousands, most end up having to have all wood redone or it wont match. What I see isn't a residue, but the polyurethane actually damaged permanently.