[Checkpoint]

Because the girl said that "the ITEM has not returned", I hadn't given her yet the tracking.

It still doesn't explain why she made the comment as per below. It's completely Inaccurate to solely rely on the label as a form of delivery confirmation.

because you actually have to put an identifying label on the package, so that they can assign the item to your order.

Just to clarify things, what does this relate to?

this means that the girl would have said "the item hasn't arrived" even if the warehouse had received, registered and stored the package.

I'm sorry, I realized I was not clear enough.

Basically as per the company instructions you had to insert inside the package (sorry, I was mistaken, the additional label was to be put INSIDE) an identifying label with a barcode which probably once scanned tells the warehouse that "the ordered and returned item" has come back.
Of course, there was no such thing inside the package.
The lady checked my order number and my order return number. It stands to reason that the system would have told her if the item had returned only if they scanned said identifying barcode which you have to put inside the package.

This extra barcode is, of course, completely different from the tracking number.

This is why I made the posts above. They could have the package in their hands, but since they couldn't have scanned the special identifying barcode, the lady would have told me that in any case.

We'll see next week when their investigation ends.