Battery manufacturers would need to provide a scanning mechanism to record the battery serial - given how low the cost is for their product, this would be prohibitive.I would think they record each battery serial pair with each phone.
I'm just guessing here though.
What companies do that manufacture products such as this is record the batch information from their suppliers for each production run - that way if issues are identified with batches from their suppliers, they can identify which of their production batches they were incorporated - and print out reports of the shipments and the list of serial number for the customers (typically carriers) to run with.
If there's actually a direct retail customer to manufacturer relationship, you'd also be able to generate those reports and automate mailings to the customers.