Change ownership of old MacBook Air

The best move would be to wipe and reinstall the macOS. They should also make sure to remove the device from their device list so that you can add it to yours.

Start up your Intel-based Mac in macOS Recovery

1. Restart your Mac.
2. Immediately press and hold one of the following key combinations until you see the startup screen:

• • Command-R: Start up from the built-in macOS Recovery System. Use this key combination to reinstall the latest macOS that was installed on your system, or to use the other apps in macOS Recovery.
  • Option-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall macOS and upgrade to the latest version of macOS that’s compatible with your Mac.
  • Option-Shift-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall the version of macOS that came with your Mac or the closest version that’s still available.

1. If you have multiple volumes on your disk, select the volume you want to recover, then click Next.
2. If requested, choose an administrator account, click Next, enter the password for the account, then click Continue.
3. In the Recovery app window, select Disk Utility, then click Continue.
4. In Disk Utility, choose View > Show All Devices.
5. Select your startup disk on the left, then click Erase.
6. Click the Format pop-up menu (APFS should be selected), enter a name, then click Erase.
7. After the disk is erased, choose Disk Utility > Quit Disk Utility.
8. In the Recovery app window, select “Reinstall macOS,” click Continue, then follow the onscreen instructions.

And here is how to remove the device from the devices list (which is something they should be doing.)

https://support.apple.com/en-us/HT204074