Pour 1 pint of hot water into a jar safe for microwave use. Add 2 to 4 teaspoons of oxalic acid crystals to the water and stir with a spoon. You must keep the oxalic acid mixture warm at all times during the following process. Reheat the mixture in a microwave oven if necessary, heating on "high" at 30-second intervals.
Dip the bristles of a clean paintbrush in the warm mixture and brush the mixture directly on the dark rings. Let the oxalic acid mixture dry on the rings.
Repeat the previous two steps until the dark rings are no longer visible.
Dissolve 2 tablespoons of borax in 1 pint of lukewarm water. Mix the powder and water with a spoon. Wipe the wood furniture with a cloth dampened in the mixture. The borax will neutralize the oxalic acid and stop the bleaching process.
Wipe the borax residue off the wood furniture with a damp cloth and dry with a soft towel.