After his reversed weaves were detected, he specifically says that al Thor must have a ter'angreal that detects saidin.

He then goes on to say that he had never heard about such a device, but that he can understand that it would have been highly sought after during the Breaking - after he himself had been imprisoned.

Demandred didn't encounter the weave unravelling hairnet or the well, hence he wasn't referring to it.

Also, Cadsuane has a whole bunch of stuff in her hairnet. They seem to be a collection of random angreal and ter'angreal. The "paralis net" seems likely to refer to the "net" in her hair itself. The little bird ornament is something seperate, as are some of the other stuff she's collected, no doubt.