Can I restore a backup from iTunes iCloud to a thumb drive or only to another phone?

I'm trying to find an old backup from the "Notes" app. I don't want to restore the whole backup to my phone because I'm looking for specific information in the backup. I had to replace my phone because of damage. Before I sent the damaged phone back to Apple, I backed it up to my iTunes account. Then when I received the replacement phone, I restored the backup. Then I did a clean up of my phone apps and contents (too many years of stuff I didn't use anymore), did a new backup to my laptop in iTunes (not to iCloud). When I looked at my note app on my phone, everything was gone.

I'm wondering if I can do a backup restore from the iCloud backup to a thumb drive or a DVD, try to at least find the info lost, print it out and manually reenter it on my phone? Anyone with steps on if and how I can do this?