Sadly the Mozy app only lets you view files your computer has backed up. It does not allow you to backup any files on your iPhone (or any mobile device). If you are able to you could try and transfer the notes to your computer and then select them for backup. Up to you to find out how to export/import those files from your phone to the computer, if it's even possible!
Past that Happy Holidays!
Benjamin_C ~Mozy Support
PS: If a response has resolved your issue, please mark it as a solution to help the Mozy Community!