If you don't want some of your fields on your form to show up in the left sidebar search tool, you can add "__" as a prefix to the field name.
So if your field name is "Project Assistant", writing "__Project Assistant" will make the system ignore your field while showing the fields available for querying on the left sidebar.
Please note that this does not make your field entirely invisible while doing queries. If your field is selected to be displayed as a column in the listing page, or if a user searches for the content in the top search bar, the results will still be displayed.