How to stop a restart of an expense report workflow from triggering On Terminate Notification?

We are increasing the Prepay Audit limit which will require a restart of the workflow for expense reports that are in-flight when the limit change is made.  Currently a restart of expense report workflow triggers the On Terminate or Send Back for Revision notification to go to the Submitter.  This notification is not appropriate and causes confusion since the expense report is not being returned to the submitter.  Is there a way to stop this notification from generating when workflow is restarted?

We will restart and then re-assign workflow that routes to the error step due to the changes in the workflow limits.  Are there other suggestions on how to handle the in-flight expense reports that do not involve restarting the workflow?