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Try a microfiber towel.

Some soaps leave more residue that others.

I have been using a tub of Mitchell’s Wool Fat and noticed a lot of residue in my sink.

Try a different soap and see if it makes a difference.

If you are not wiping down your blade properly, all that residue, soap, skin, blood and oxidation,(rust) is getting on your strops.
Rinse in hot running water and then dry with a microfiber towel,...