If you imported or entered a trip you want to delete for any reason simply tap a line item in the duty header.  The duty editor will appear and a red button at the bottom will allow you to delete as needed.  If your duty period is in the past it will be locked, tap the lock button on the upper right to unlock and then you can delete the sequence.  For more details refer to the following link in the documentation which includes a tutorial video.
http://docs.nc-software.com/display/APDLDOCS/Delete+A+Trip