Can't Restore From An Old Backup

I have two devices here. An iPod 6th gen on iOS 10.2, and an iPhone 5C on iOS 10.3.3, with no SIM card.

I'm trying to restore the iPod 6th gen to a backup previously created on this iPhone 5C.

I plug the iPhone into iTunes, and the backup shows up under "Latest Backups," and says it was backed up "to iCloud" in 2017 (the backup I want.) But when I check any other device, including the iPod, this backup does not show anywhere. I see my other backups for other devices, but not this specific one that only shows up when the old iPhone is plugged in.

I may be confusing myself too much, but I've read up enough to understand that you can't back up to a backup that wasn't made on the same version of device as the one you're trying to restore to. But, I'm fairly certain this backup that I want is iOS 10.2. And if it isn't, how am I supposed to tell?

My main concern, to reiterate, is I need to restore a backup that does not show on the new devices restore screen.