Place the teak wood chairs outside in direct sunlight or inside near a sunny window. Leave the chairs in the sun for two to three hours to dry out the mold spores.
Vacuum the teak wood to remove the dead mold spores, using an upholstery attachment. Discard the vacuum bag immediately afterward to avoid transferring mold.
Fill a bucket with 1 gallon of hot water. Add 4 tablespoons of dishwashing detergent and 1/4 cup of bleach.
Wet a sponge in the detergent and bleach solution. Wring out the excess solution. Wipe off the teak wood chairs to remove any remaining mold spores and stains. Rinse the sponge as needed throughout the washing process.
Dampen a clean cloth with water. Squeeze out excess moisture. Rinse the teak wood with the damp cloth to remove the soap solution.
Dry the teak wood with a dry cloth. Add a quarter-sized amount of teak wood polish to a clean cloth. Rub the polish into the wood to restore moisture and protect the wood.