I believe you should be able to connect your iPad to iTunes and select "restore from backup.". You'll lose any new stuff you've put on there since that backup, but you should be able to get that note back.
I say that because usually, you can "dig into" iTunes backups - they are all or nothing affairs. However, you could look into a program called iBackupBot that allows you to sift through iTunes backups. I used it once to find a password (caution: I used the paid version, not the free trial version). No guarantees, but maybe it's worth a look?
Hopefully, either one of these may help - or someone will be along to help with another idea. Sorry for your troubles and good luck.
Marilyn