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Get a rag or soft cloth damp with warm water. Use the damp rag or cloth to wipe down the cork. Try to loosen any dirt while you wet the cork. Wash your cork directly under the faucet tap. Do this for cork that you are prepared to get fully wet, like a fishing rod grip. Don't leave standing water on cork floors. Also don't submerge shoes with cork uppers or heels under water. This could ruin any leather or suede on the shoes. Use a damp sponge, gently scrub a soapy cleaning solution into your cork. Rub in circles and clean the entire surface. Rinse the cleaning solution off of the cork. Finally, dry it with a clean, soft rag or allow the cork to air dry overnight before using. Clean smaller cork items with mild detergent and water, the vinegar, soap, and water cleaning solution above, or store-bought cleaners. Make a paste with Borax to remove tough, ground-in dirt. Combine water with Borax in a shallow bowl. Start with about ¼ cup (60 mL) Borax and add just enough drops of water to make a thick paste.

Summary:
Wipe away dirt with water. Put your cork under running water. Wash other kinds of cork with a cleaning solution. Make a paste with Borax.