When viewing a user's logbook sometimes the fields may appear greyed out or you may be unable to delete the logbook. This will be because the logbook is pending approval and it cannot be amended until it has been approved.
If the logbook is still pending you will need to approve the logbook before you can go back into it to edit the text. Once the logbook has been approved you will be able to edit or delete the logbook unless it has lock editing enabled.