When we took on (re-took) our plot a few years ago, the carpet was a mixture of all sorts of rubbishy stuff, and almost totally interspersed with couch and dross. It was like steel wire!
I had to literally dig it out with a spade after trying to cut it loose with a Stanley knife, and luckily, we all had a rough place on an un-diggable plot well away from everyone else which was too far gone, with some trees even about 8" in diameter! This was where we all managed to stick such items, because we really needed it! (It grew some great comfrey though)!
The carpet hadn't killed the couch grass, just nurtured it, and I think I mentioned years ago, how long it took to clean the plot - around an hour a square yard.
Never again Pedro!