Do you mean the search history where it auto completes what you type in the search bar?

If you don't want the history to show then go to Tools>Options>View>Autocompletion> then untick the box that says "Enable autocompletion of Text Fields" then click apply. Also when you shut LW down the search history is erased.

If you mean the little checks that show in the search results. They indicate files that are already in your library. You'd have to move them out of your library for the checks not to show up.

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