If your hay have turned into extra dusty recently and the discharge is not colored and only slightly wet around the nose. Also if he don’t get stuffed nose or trouble breathing. I wouldn’t stress all too much. Try to dust the hay before giving it to him. But do a check up to rule out other problems.
It’s good checking out, my own bunny get that stain often. Turn out he’s sensitive to something in the hay that trigger snuffle/ a runny stuffed noise. But when he live outdoors he won’t have the same problems as indoors. I think the wind blow away the dust and give him a top ventilation which help his sensitivity to hay. He have chronic rhinitis, so stuffed and dirty nose comes and go. Right now he have a white clean nose but will sneeze after being near his hay and get a little bit stuffed.