Soak the print in pure water. If the water stain is caused by water, you may be able to remove it by making the paper behind the print uniform again. Use clear, cold, pure water, and make sure that the print lies flat in the tub.
Let the print dry. Place it on a flat surface like a table and let it dry. Examine it in good light to see if the water stains are gone. If they are not, then move to the next step.
Mix a weak bleach solution, using 50 grams of the chloride of lime and a quart of pure water. When you pour the solution into a tub, use one part of this solution for 20 parts water. Wear gloves from this point forward to protect your hands.
Soak the print in the weak bleach solution for two hours. It will not damage the ink, but it does have the potential to make the paper brittle, so be sure to test if you are concerned about the quality of the paper. This should brighten the print and remove the water stain.
Soak the print in a bath of weak acid. Generally, this bath should only last a few minutes, but consult the specific acid's instructions to avoid damage to your print. This bath will neutralize the chloride of lime. Use a print-cleaning acid from an art store, and do not attempt to make it on your own. Follow the instructions for mixing and soaking exactly so that you do not damage your print.
Soak the print in clear water for three hours. Once finished, you can dry it once again on a flat surface, and the water stains should be gone.