[Esel Mann]

The most practical thing would be wipe/clean the jacket/stress reliever, and slide it back. Use isopropyl and a thin cloth. Wrap a flat bladed (aka common) screw driver with the thin cloth
if necessary to provide stiffness if scraping is necessary. Replace the RJ-45 plug with a new one, slide the jacket/stress reliever back to original position. Home Repot or bLowes should have home DIYer RJ-plugs. Depending upon the type they should also have the tool that pushes the contacts into the wires.

That aside (and this can be done as I've had to do it), first open up a can of patience. Do before 5pm HH so beer is not a requirement. Next clean the outside jacket/stress reliever like above. Slide/wiggle it back. Now turn attention to the plug cleaning the outside of it like above. One can also use (carefully) a razor blade or xacto to scrape.

Now the contacts. Those can be done by carefully scraping the contact within the channel using the non blade side of the xacto blade point and isopropyl. Do not deform the contacts.

Then use air (tech-in-a-can or from a compressor if you have one) to blow it all out and evap any remaining isopropyl. Slide jacket/stress reliever back on. Walla.