I am old enough to remember when a lot of machines had grease cups and my father sold cup grease. Every grease cup that I can remember had some kind of fiber disc that would limit the amount of grease while not scratching the shaft. Parts houses carried these discs in generic sizes. Plastic as we know it now had not been invented yet. Most of these discs looked like the same material as the rubbing block on points of that day. The disc had limited life and had to be replaced occasionally. These discs were strictly to limit the flow of grease and had nothing to do with stabilizing the shaft. Cup grease was about the consistency of Crisco shortening. It was a totally different consistency than chassis lube or wheel bearing grease.