You cannot delete books using CC while connected because there is no way for CC to tell calibre to remove the book from calibre's device view.
However, you can use calibre to delete books from CC while connected. If you want to delete the book from both CC and calibre then delete the book in calibre's library view. Calibre will ask you whether you want to delete the book from the device (CC), from calibre, or from both. If you want to delete the book from CC but not from calibre then you can delete the book on calibre's library view and select "from device", go to calibre's device view and delete the book, or disconnect CC and delete it there.
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