Deleting Your Internet Explorer Favorites. 1  Click on the Internet Explorer Favorites icon, and select Organize Favorites. 2  Select the Favorite you want to delete, and click on the Delete button. 3  You'll be asked if you are sure you want to delete this; click Yes. Click on the Internet Explorer Favorites icon, and select Organize Favorites. 2  Select the Favorite you want to delete, and click on the Delete button. 3  You'll be asked if you are sure you want to delete this; click Yes.