RE: Quicktune drop away rests
Does it make the noise when you simply pull on the cable?
Does it make the noise when you draw the bow without an arrow nocked?
If you said yes to either of these then it is inside the rest. A small drop of oil will probably take care of the problem but you could also call NAP and I bet they will send you a new on ASAP.
Are you absolutely 100% sure it is the rest. Could it be the cable slide?