When an instructor gives the TA only 'new' permissions, the TA also sees the 'grade' link, the 'duplicate' link, and the 'remove' column with the update button.
The TA can't actually grade the assignments, the 'grade' link takes him to the 'student view' window.
It would seem to the TA that the 'duplicate' link does nothing, but when pressed, the instructor does see a copy of the assignment. If the TA is supposed to be able to duplicate assignments with the 'new' permission, then he should be given a notification that he has done a duplication.
The remove column does not have the checkboxes for the assignments, so the TA can't remove assignments. But the 'update' button appears, and when pressed, it gives a warning message that an assignment box should be checked first. Since the TA has no 'delete' premissions, than he should not see the remove column or the 'update' button.