You must have delete access to a planner in order to be able to delete its bookings.
To delete a planner booking from the planner, select the booking and press the Del key on the keyboard. OfficeTalk will confirm that you wish to delete the booking.
To permanently delete the planner booking, depress the Shift key and then press the Del key. OfficeTalk will show a different confirmation.
For more information on deleting items, see The Recycle Bin.