There it is...............
Does anyone out there remember 'cotton waste'? It was huge bundles of waste cotton thread, presumably from the northern cotton industry, who bundled it up to use in much the same way as we use old rags now. You pulled a hand sized lump off (or cut it off with an old pen knife.....) The trouble was that if you used it to wipe your lathe, milling machine or drill down, hundreds of razor sharp shards of steel would get impregnated in the bit you used and the next minute, when you wiped your hands with it.............. a razor sharp cut would appear.
In the Mortar context, the cotton waste was wrapped around the bore brush and used to scrub and oil the mortar barrel