Is she eating canned food or dry food when this is happening?
Or do the tears run all the time?
Is she a persian type cat with a flat face?
This is probably from her eyes watering due to possibly injury, infection, lashes rubbing on the eyes or the result of an upper respiratory infection leaving the tear ducts clogged.
What happens is clear tears run down over the face leaving the fur damp. A bacteria grows on the fur and that bacteria gives off an iron oxide as a waste material that stains the face where the tears run a reddish color.
Cats can also have a sebaceous gland issue that causes build up around eyes, nose and in some cases mouth and chin which you can see here
http://www.fabcats.org/owners/skin/acne.html
This site goes over the red tear stains and the picture is of a dog but the same applies to cats
http://www.peteducation.com/article.cfm?c=2+2092&aid=1156
Hope this helps you!
PS as you said she looks scratched this may indicate eye infection or injury is causing the excessive tearing. Best option would be a vet visit if you decide the cat is going to be yours.
Cat Health, Behavior, Care Expert
30+ years cat owner, rescue, breeding, study of behavior & health care