Muting Audio on synchronised clip

This is the camera with the audio or the one above?

Neither of them seem to have audio. Or is the camera audio inside the detached sync audio? If the camera audio is embedded in the detached sync audio, I think you're stuck having to do it clip by clip.

You should open the Synchronized Clip in its own timeline and bring down the volume of the video clip.

As an aside: you DON’T need to detach audio in order to make J- or L-cuts. Use Expand Audio instead. It keeps video and audio together, keeps the timeline neater.

I understood from your message that the echo was being caused by the audio embedded in the video file. Is that detached as well as part of sync clip? It might be helpful if you showed some screenshots of the state of the timeline and the audio configuration the inspector.

Select all the video clips and in the Audio inspector go to Audio Configuration and uncheck the tracks you don’t want.