Cover the area with dropcloths. Set the white wicker on top of a dropcloth.
Brush the surface of the wicker with a soft-bristled scrub brush to remove dust and debris.
Fill a plastic bucket with 2 cups of cold water. Pour 1/4 cup of gentle dish soap and 1 cup of white vinegar into the water. Mix the ingredients well.
Saturate a sponge in the foamy mixture, and start scrubbing the top of the white wicker. Scrub gently while moving downward toward the bottom of the piece.
Rinse the mixture from the wicker with cool water. Flip the wicker over and repeat the process on the back side.
Remove the excess moisture from the wicker with a towel. Let the wicker air-dry out of direct sunlight.