Deleting an old search you no longer want to use is simple with Open Opportunities.
Your saved searches are listed in your settings, to delete a saved search, all you have to do is go to your settings, select the search you want to delete and then confirm that you want to delete it.
To go to your settings page, hit the cog icon ⚙️ in the top right hand corner of your screen (on mobile you select the three lines to bring up the menu and then select settings).
Once in the settings page you can see your saved searches listed. Expanding the leading pointer will allow you to see the details of the search, so that you can check what features are part of the search.
To delete the search, hit the Delete button for the correct search and then confirm that you wish to delete the search in the subsequent popup.