Before I took my car to the shop, I noticed there was a thick, shiny, space age foil-looking wrap around the muffler. When I got my car back, I noticed they didn't put that wrap around the new muffler. What purpose does the foil-type wrap serve and is it a big deal that I don't have it anymore?

Also, what is that strange metal loop that drops down visibly under the back of the car?