Padraig, it's coming back to me now mate... yes you need to plug the loom into the amp!
You also need to connect the pink wire into the back of the stereo block connector. I can't remember which pin, but the wiring loom supplied should have a spade connecter on the end of the mute wire which should slide inside the existing cars block connector.
The diagram should tell you which pin it goes into? That will mute everything including the amp.
At the moment the telemute module you've probably got is forcing the speakers to mute, but not the signals from the amp. The mute wire will kill the audio to everything. It's quite easy actually, just sounds hard to do.