Once a note is added to a contact it cannot be edited or deleted. If you would like to see this functionality within your account, feel free to vote and/or comment on the idea here in the Feedback area. Make sure to take a look around and vote on other ideas that you like or suggest new ones!
I think the contact note section should be editable or deleted as necessary. Once it's there, it's there and if that field is exported causes to many revisions on my end. Not efficient at all.