If all that's holding those damping pads is the staples I see, I'd remove as much as I could get to and replace with NoRez. NoRez works best when the damping layer in in intimate contact with panel. Not magic, just physics.
If they happen to be glued in addition to staples, it would be more work because whatever glue remains would need to be removed. The PSA on NoRez is aggressive, but has no ability to fill gaps, hence the "intimate" rec. Clean surface is also important. Adhesion is only as good as weakest link in chain and if that link is debris, it will be a lesser bond.