What permissions do I need?
To close searches, you don’t need any other permission apart from that required to run searches, at least the View level of the Finders permission (visit Run a search using a finder to know more).
From the search window
Close a search by clicking the Close Search button on the search window toolbar.
From the Navigation pane
Or you can also click the x of the running search under the Data Search option of the navigation pane.