Tear staining is caused by a chemical and bacterial reaction of the proteins in the hair and the tear. The odor is produced by the bacteria. If the area is not red or swollen and if it is not bothering the dog it is something you can treat at home. Here is some additional information for you:
Tear staining is caused by a reaction between the chemical nature of the tear and the proteins in the hair. The chemical makeup of tears varies from dog to dog, that is why some white dogs have no problem and others do. There are cleaning type products available but they rarely work. The most reliable products are added to your puppies food and act by changing the makeup of the tear. These products can stop further staining but the already stained hair has to grow out which means you must use the product for a month or so before you see the full benefit. Two of the more commonly used products are "Angel Eyes and White Eyes" There are also several herbal products now available. These products are safe to use and will work for the majority of affected puppies.