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I assume you are referring to the edited submission using an edit link or in the "Submissions" page, if that's the case, I believe the people or those in the recipient email addresses will also received a notification when the edited submission has been submitted, this is because you are just re-submitting.
Here's a guide regarding how to edit your submissions: http://www.jotform.com/help/325-How-to-Edit-Submissions-Made-on-Your-Forms.
If I misunderstood your concern, please let us know.