You can configure the fields that are displayed, as well as the displayed order of your fields under the left sidebar search tool.
Click on the gear icon underneath the Search button. From the prompt window, you can remove fields that are displayed on the left sidebar search tool by adding them to the "Available Fields" section. This would not remove the fields from your listing page or form page design. You can also adjust the order of the fields that are displayed in your left sidebar from the "Selected Fields" section. Click "Save" to save your changes.