Clear Retained Charts:
To delete retained birth charts, highlight the charts that you wish to delete, then click the delete retained toolbutton at the top of the main window:
Alternately, you can use the menu item Chart | Clear Retained or hold down the <Ctrl + Del> keys on your keyboard:
This does not get rid of the birth charts that you have saved, it only keeps them from showing up every time Delphic Oracle starts.