The MeteoSwiss app automatically displays the five most frequently used locations on the home screen. These are locations you have searched for, use frequently, or have visited (only when location services are enabled). If you no longer want one of these locations to appear on the home screen, you can swipe it to the left to remove it. The current location (when location services are enabled) is the only exception.
You can also add fixed locations yourself and change their order in the settings under “Your locations.”
If you do not want the app to suggest locations, you can disable “Locations based on your usage” here.