… I want to delete a fermata from my score but not from the palette …

By your word ‘palette’ I suppose that you mean the Articulation Selection dialog box, right?

To remove an item from the score, switch to the Selection Tool, and double-click the item.

Double-clicking the item will take you to the tool that entered the item (in this case probably the Articulation Tool), with the item selected so that you can remove the item by hitting the delete key.

… Why would I want to delete it from the palette? …

Again, by your word ‘palette’ you probably mean the Articulation Selection.

In the Articulation Selection there is a Delete button that lets you delete an item from the entire document.

This step will decrease (a little) the document’s data size.

You would want to delete an articulation from the Articulation Selection if you do not need the articulation, perhaps because you have another articulation that looks better.

Finale will warn you if the articulation is in use in the score, and offer you the option of (in the score) replacing the articulation with another articulation.

… What am I missing here? …

My guess is that you are missing the difference between removing a selected item from the score (by hitting the delete key), and deleting an item entirely from the document’s stored data (by clicking the Delete button in Articulation Selection).