My oldest, the one mentioned above, is around 10 years old and has never had anything on it, just like my other Kanoyamas and a Tony Miller. They’re just like new.
There are two reasons for not treating a strop. One is that I don’t want anything between the razor and the leather, I want steel hitting clean leather. Leather treatments are either oils or waxes. If you wax your strop, you’re stropping on wax, not leather, at least to some extent, until it wears off.
Second, a strop does not have to be protected from anything (except us and our ’treatments’), it isn’t a shoe, a glove, a coat, or anything exposed to water and the elements. Using a strop will keep it supple.
I do occasionally use oil or strop paste (fat) on a stiff, dry eBay strop, but I use that mostly on the back, then let it hang a couple of weeks and repeat until it’s limber again. If a strop is limber and not shedding leather dust when you strop, oil or fat isn’t needed.
I also maybe once a year, wipe mine down with a damp rag to remove accumulated dust, etc. Wiping with a damp rag will raise a little nap too, and if you like that it’s fine and will wear down with use. You can also rub it with your nagura or jnat to polish the leather, but you’ll need to lap the jnat/nagura after each strop polishing.
If you want a chuckle, Iwasaki, in his chapter for barbers, describes how to clean a strop that's had too much ’protection’. First, soak it in gasoline for a day or two to remove the ‘strop treatment’. Then wash it two or three times in warm soapy water to remove the gasoline. Then rinse it two or three times to remove the soapy water, working the leather. Lay it on a flat surface and roll a bottle over it a few times. Then dry it for a few days between two flat boards to keep it from curling. If needed, then sand it with ‘strop paper’, around 800-100 grit sandpaper.
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