I invented the process on the fly with what I could find.
I dumped the dirty, encapsulated walnut grits into an old pillow case, submerged that in a sink full of hot soapy water, and kneaded the heck out of it for a while. The water turned black. I let that water out and refilled the sink with more hot soapy water and repeated the process. The water turned brown. I let that water out and filled the sink with hot rinse water and kneaded it all again. The rinse water turned kinda murky, but was getting much better.
I rinsed the bag full of media real well under the faucet for a while until the water running out was not very dirty at all. I then carefully dumped the soggy mess out of the pillow case into a bag temporarily made of some plastic mosquito netting. I rinsed that real well to wash away all the little stuff, leaving only the full sized media grits.
I dumped the cleaned media out on a large aluminum foil oven liner sheet to dry. After it was dry I looked at it under a magnifier, and it looked brand new - like a bowl of Grape Nuts cereal.
I put the dried media back in the tumbler and ran about 900 cases of different kinds through it, and that media polishes like brand new stuff. I'm sorry now I threw out the first 1/3 of that gallon jug years ago instead of trying to clean it.
I don't use any kind of polishing compound in my walnut media any more. That's what happened to the first batch - ruined it. This batch got encapsulated over many years with traces of sizing lube, etc. I now only use polishing compound in some coarse pet store corn cob media.
I don't use One Shot or any other kind of lube that can be tumbled off. To me, the idea of using tumbler media to
remove anything other than powder residue and general dirt residue is crazy. Those folks are the ones that drive the tumbling media replacement market.
So, my original gallon jug of walnut media will last me my entire life, by simply not polluting it and by an occasional cleaning at 20 year intervals.