Vinegar. iStock/Thinkstock. To remove white rings left by wet glasses on wood furniture, mix equal parts vinegar and olive oil and apply it with a soft cloth while moving with the wood grain. Use another clean, soft cloth to shine it up.To get white water rings off leather furniture, dab them with a sponge soaked in full-strength white vinegar.inegar. iStock/Thinkstock. To remove white rings left by wet glasses on wood furniture, mix equal parts vinegar and olive oil and apply it with a soft cloth while moving with the wood grain. Use another clean, soft cloth to shine it up.