When a linked file which contains a Scope Box is printed the Scope Box border will print. This will happen even if the 'Hide Scope Boxes' checkbox is ticked.
As a workaround you will need to hide them in each view by using the Visibility/Graphics Overrides box.
Please note that you can override the visibility in the element properties of the Scope Box. If you turn it off in every view you will not be able to click on it again to edit it.