Pour scratch remover or furniture polish on a soft cloth and rub it into the scratch. Wait a few seconds and then gently buff the area until it shines. This usually makes very fine scratches disappear.
Dab a cotton ball in iodine and rub it into the scratch to remove it. Dry the area with a paper towel.
Dab some solvent, such as lacquer thinner or denatured alcohol, on an inconspicuous part of the wood furniture. Wait for one of the solvents to soften the wood's finish. Use a small paintbrush to spread the appropriate solvent across the scratches, using diagonal motions. This blends the scratched area in with the rest of the wood.
Mix equal amounts of powdered pumice and mineral oil together in a bowl. Dab a piece of extra-fine steel wool into the mixture. Use the steel wool to gently apply the mixture to the scratch. Clean the mixture off the wood with a cloth or paper towel.
Boil a small pot of water and place a bag of black tea in it. Let the tea steep until the water turns dark. Use a thin cotton swab to apply the tea to the scratch.
Blend together a small amount of water and instant coffee to create a paste. Apply the paste to the scratches to conceal them.