I can think of two potential causes of this symptom, and I don't think either one would be related to tooth grinding. Grinding your teeth is something that you probably wouldn't be aware you were doing, and it would only know if someone else heard you doing it or if your dentist
saw some evidence of wear and tear on the teeth at your regular dental checkup.
On the other hand the salty taste could come from acid reflux
. When acid from the stomach washes up into the esophagus and mouth, which commonly happens at night when you lay down, this can cause irritation to the back of the throat, cough, and a bitter or salty taste in the mouth when you wake up.
Similarly, nasal allergies or sinus congestion can lead to drainage of mucus down the back of the throat, which is usually worse at night. This can give the same sensation of something salty or bitter in the mouth.
I suggest that if this symptom persists that you go to see your primary care doctor
. They will be able to due a quick exam and help you sort out what is going on and whether you should take a medication to help.