Howdy,
It's a very simple operation, assuming the rope is new enough that you can open the cover to get at the core. You'll find details on the procedure in the "Apprentice", and maybe better ones in our "Basic Braided Splicing" book. But it's essentially a matter of loosening the cover, then using an awl to make a space ó gently ó to get at the core. Be sure to tie a Butterfly knot in the standing part before pulling the core out. Cut core square a little beyond where it emerged, then cut a short taper on it, before pulling it back in.
If you can't get the core out, try washing the rope. Still no luck? Replace it.
Fair leads,
Brion Toss