Wipe the leather top desk with a dry cloth to remove surface dust, dirt and other debris.
Dampen a clean cloth with water. Blot the glass rings with the cloth. Dampen the leather with the water. Allow the desk to air-dry. If the water rings are still visible, continue with the remaining steps.
Saturate a sponge in white vinegar. Wring out the excess vinegar so the sponge is damp but not dripping wet.
Rub the glass rings with the sponge. Saturate it in the vinegar and wring out the excess liquid when it becomes dry.
Continue rubbing the desk until the glass water rings are no longer visible. Wipe the desk with a damp cloth and dry with a towel.