For my #70916 order, I was able to get a refund adjustment for the price difference ($19, $64 vs $45) after sending a polite message to Amazon CS.
Either I got lucky, or Amazon still does price matching under specific situations (like, when the order is still in the warehouse and cannot be canceled). So, if a similar situation happens to you, I'd definitely give a refund request a try.
(And, apologies to Astrobrick for not seeing your post before my last post.)
*Minor variations, such as differences in moulds (that Bricklink officially recognizes) or part colors should usually show up as "Alternate" parts in a Bricklink inventory (BL Help page).
As to what prompted the question, does your version of the box not show the part count? Or, the potential buyer could be a new or casual Lego buyer who does not how to check the Lego site or third-party sites (Brickset/Bricklink) for this information. And, it could always be a customer just testing to see how friendly and/or professional you, the potential seller, is.
In your response to the customer, I would mention that Lego's official count (1032) includes the brick separator tool,** but not any spare/extra parts that may be left over after the set is built.
**Which Bricklink considers an "extra" item, so its parts count of 1031 lines up correctly with Lego's official count.