The NLA editor is complex I strongly recommend read the documentation. I will show how I cleanup the references to an action.
Blender NLA Doc
First you need to clean up the reference by deleting the tracks (start icon), select the Plane.002 ActionStrip and the NlaTrack Action and press X to delete it (be sure to only select the ActionStrip and the NLATrack), Repeat the process for Plane.001 and Plane ActionStrip
Next select the ActionStrip Plane.002 and delete the Action by hold Shift+(press the icon) X. This will delete the reference to the Action. Repeat the same for Plane.001 and Plane ActionStrip
Note how Blender will warning you about the 0 references and that the Action will not be saved at the top most bar (or status bar near the windows title)
Finally save and re-open the file:
I can only summarize that you can save an Action an apply that Action to another object Note how I apply Skate -> Skate.001Action ActionStrip to Plane.002 object. The number 2 next to the action indicate that the ActionStrip have two references. the NLA does a lot more things.