A couple of things you might check;
First, remove the arrows and see if the noise is still there. Might be the shafts are not tight in the grippers. A bit of Liquid Tape applied with a Q-Tip to the grippers can tighten things up. Another possibility is that the broadheads are pushed all of the way thru the foam and contacting the cup. A couple of layers of MoleSkin up in the cup might help.
If the quiver still makes noise without arrows in it, you might try checking to make sure the connections are tight. I have a Bear Quiver with the spring arms that I quieted down with self adhesive bandage (cheaper in the pet section than the Pharmacy) by wrapping under and over the arms. Another time an old Sagittarius quiver was found to have a loose rivet.
Failing that I would contact the folks that made the quiver. 99.99% of the people in the Trad business will go out of their way to help you out.
Good luck & please let us know what you find.