If you run a tool and realized you made a mistake and need to rerun with a modified parameter you may not be able to simply use the open and run commands in the ArcToolbox results tab because the output already existed. You could go to ArcCatalog and delete the original output, or be give the output a new name (leaving the incorrect original there). You could also right click on the instance in the results tab and click delete but this deletes the historical instance of the tool run as well as the output. Why can you just right click on the historical instance and Delete The Output only then right click Open and run the tool the way you want. In other words add a "delete output only" choice to the context menu for ArcToolbox results tab.