I believe it’s supposed to be either / or. Order number, or email that tied to order number or photos of the Mainboard serial number. This being due to Framework supplying a CMOS battery replacement regardless of warranty, and regardless of whether it was bought new or used. If bought used, you would not normally have the original order number, and you may no longer even have contact with the seller, presuming they would even be willing to find the order number for you. Similar to the procedure for the CMOS / RTC battery replacement module, which is outlined on Framework’s github.
From Framework’s github
github.com/FrameworkComputer/RTCRework
Requesting an RTC Battery Substitute module
If you have an 11th Gen system or Mainboard, you can now reach out to support to request a free RTC Battery Substitute module. To make the request process go smoothly, enter the email address that you ordered the 11th Gen product on and/or include photos of the system and Mainboard serial numbers.
Note that there are no constraints making this request other than being an 11th Gen system or Mainboard owner (whether or not you are in warranty). We ask that you really make sure you are comfortable with performing soldering on expensive electronics items before performing the installation, as we won’t be able to provide advice or support around soldering or provide fixes for failed soldering attempts. We also ask that you only make the request if you’ve faced needing to perform a Mainboard reset, as we want to avoid waste.
Commit history for the text (the readme.md file) says upload and edits are by Nrp.