That would depend on whether the user is part of a security group that has the rights to delete a Notification.
-Log into AyaNova as the AyaNova Administrator (or a user that has full rights to Users and Security Groups)
-Select the Administration navigation pane, select the Users grid
-Open the User entry screen for the user that received that error and confirm what security group they are a member of
-Exit out of that User entry screen
-View the Security Group grid and select that security group that user is a member of
-Is the Security Level for Object.Notification set to Read/Write/Delete?
-If it is not, than set it so, and save.
-Have the user log back into AyaNova and now delete that notification they wished to delete