There is a role restriction named Notebook Item Delete which prevents users from being able to delete any Notebook item. Check to see whether the user account has this restriction listed against a role in which the account sits. by following the below steps:
From the Ribbon, click Options then click Manager.
Click Role Maintenance.
Check if this restriction is added into a role with the user account listed.
If this restriction is in a role where the user is listed, you can either;
remove the user from the role.
remove the restriction from the role.