You can restore the notes from the backup you made in iTunes using a program called
iPhone Backup Extractor
Use my link below to download the program so you can install it
It is free for up to 4 files so you wont need to pay for it.
Once installed on the computer you made the backup on, the application will automatically look for iTunes backups located . If you have multiple backups, you can select the one that contains your notes, from the drop-down menu 'Select backup'.
To extract your lost notes, look in the 'Available data' section and click on the blue link 'Extract', next to Notes.
Choose the destination folder where you want to extract your notes and then click 'OK'. The iPhone Backup Extractor will recover all your notes and deleted notes from your iTunes backup.
You can then view the note
If you have any problems, or would like any additional information or assistance, please do not hesitate to let me know.
Else if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.