Playing with a camera path, don't like the way it turned out, and want to try again. How do I reset/remove the current path?

Do you mean with using the Camera Path Editor tool? 
I have some issues with that at the moment that I am trying to solve, I don't know if it existed in Apr 2020. I am a new user. 

Have you learned how to do pathing? 

My problem; I have set out a path going around the earth, then moon. At the moon I lock the position so you see that the moon keeps facing the same side towards earth, while it's orbiting. 
But when I replay the pathing, I see the path following the same directions, but Earth and the moon are in some other location.

Playing with a camera path, don't like the way it turned out, and want to try again. How do I reset/remove the current path?

To reset you create a new path (Shift + A → Curve → Path/Bezier). Add the Follow Path constraint to the camera again and assign it to the new path