I think you’re conflating the Self-Study Quiz script with the Item Inspector. To my knowledge there is some link between them, but that probably isn’t it. Here’s what you can do to make the kind of preset you seem to want:
Step 1: Open the Self-Study Quiz popup (you already seem to know how to do that, but just in case it’s in the navigation bar on the top right, at (Profile) > Scripts > Open > Self-Study Quiz.)
Step 2: Click on the light gear icon on the top right of the popup.
Step 3: Navigate to Items in the top bar and create a new preset.
Step 4: In the new preset add the filter SRS Level and select Apprentice 4.
Step 5: Save and you’re done!
*I’m not really sure how the link between II and SSQ works, to be honest, because I’ve never really used them that much.