Slime can be a protective covering and a sign of stress... or it can be a bacteria film. If it is a thin layer (hard to tell depth from a pic) then I tend to leave it. If it is thick or seems to be comming off the coral in strands I try to gently blow it off with an eye dropper or turkey baster.
He is talking about getting the mucus layer off the leather by putting a turkey baster in the water and letting it fill with water then blowing water on the leather to get the mucus layer off of it. The eye dropper does the same thing. You can even use a powerhead to blow off the leather. The carbon will absorb any chemicals released by the leather. You can get activated carbon and put it in a reactor or a filter bag and place it in a high flow area.