How do I hide certain items from structure tree when exporting to 3D PDF?

If you go to File > DesignSpark options > File Options > General, under Export options, de-select / untick "Export hidden components and geometry." By default, this option is ticked.

This way, if you have anything hidden when you save the document, they will not be retained upon re-opening the file. 

In case of 3D PDFs, the hidden item in the DSM design structure tree will not appear as part of the assembly in the PDF.