Recover deleted note on iPad2

What do you mean paid recovery downloads? I would not use a recovery service on an iPad, since that gives them access to all of your data. Most of the time they will give you some data back, and it generally is not what you are looking for. They are a complete waste of money.

Hopefully this demonstrates the importance of regular backups of data to ensure you don't lose anything, or at least minimize losing things.

Only if you are careless with iCloud and are not using 2 factor authentication, or you allow someone to have access to your computer if you have an iTunes backup. Not backing up the iPad doesn't give you access to your information either.

If there is no backup, there is no way to recover the note.

Were you using Notes On my iPad, or iCloud? Am I correct that you say you have not backed up the device? Do you see a Recently Deleted folder?