allergies, but tear stains are a caused by a red bacteria in the secretion. It is normal though not very attractive. Leo had it when we got him at 5 months old. I got rid of it in 2 weeks by putting Angel Eyes original formula in his food. I still do it every week for both dogs to make sure the stains do not reoccur.
The bacteria can only survive at a certain PH level so sometimes changing the PH level in the dogs system can also get rid of the stains. Apple Cider vinegar (with the mother, brand like Bragg) causes the PH to become more acidic. Giving the dog a Tums at meal time will cause the PH to become more alkaline. Therse are two additional remedies, though I have not tried them. For me, Angel Eyes, which is a very mild antibiotic, has worked for very dog I ever had with tear stains. Also, do not feed or give water in plastic bowls which harbor the bacteria. Use stainless steel or ceramic bowls.
For whatever it is worth, Science Diet is not a particularly good dog food. I know the vet sells it but vets are not nutritionalists. I bet a higher quality dog food will help all around. I personally feed a commercial raw diet but there are tons of people on here that feed Fromm kibble as well as Orijen and other outstanding dry do foods. If you are looking to change foods, check dogfoodadvisor for a particular brand to see how it rates. Good luck!