Hi. Using abrasive pads is really a band aid fix, by using a mechanical solution to a chemical compatibility issue. The old tether is polyethylene, a polymer known to be really difficult to bond.
A trick that can help with both this polymer and others is to do a flame treatment, where you use an open propane / butane torch to gently sweep over the plastic. You dont want to melt the plastic, but the flame must touch the plastic right before you add the resin. This allows for a better chemical bond to the polymer, and will also help when gluing other polymers. I have done multiple test with Scotchcast 2131 which I used for these things, and flame treatment has helped in all the different cables / umbillicals I have tried. The general bond strength and peel resistance were multiplied by many times in my non-scientific tests.