A cleaning cloth is made by using Karamja rum on a piece of silk, which is used to wipe the poison off a weapon or the colour off an Abyssal whip or Dark bow if one has used the recolouring items obtained from the Bounty Hunter Store.
This item can also be bought with 60 coins from Tamayu in the village of Tai Bwo Wannai, located south of Brimhaven, deep in the jungle of Karamja, once the Tai Bwo Wannai Trio quest is completed.
A fast way to make them is to buy regular silk and bank it. Withdraw it using the bank in the Tzhaar caves. Then, exit through the volcano in karamja, buy the rum (due east of the volcano, next to the karamja general store), and make the cleaning cloths. Drop the rum outside the Tzhaar cave entrance as it explodes from the heat if taken in, re-enter the volcano, and bank the cleaning cloths, withdraw 26 more silk, exit the caves and pick up the rum and repeat the process.