Reports in the Report Designer Favorites folder can only be deleted via the Save As window and only one report per Save As click.
If you want to delete more than one report, you have to click Save As, select the first item by clicking on it once, then click the X icon to delete it. After the first report disappears, close out of the window and click Save As again. You can then delete the second item the same way. That process can be used ad infinitum to delete as many reports as you want from your Favorites folder.
There is more on Report Designer shared report templates.