"Recall" / Cancelling an approval task from a source system

We are using a workflow to kickoff an approval task. The source system triggers the workflow API, we lookup the approver and send them a task. There are some situations where the submitter would want to "recall" the approval request to make a change or cancel the request where they'd click the button in the source system and I need it to update my workflow. 

I'd LIKE it to set the task status to recall to end the task and move to the next step of updating the DB, etc. but I'm struggling to find a way to do this. If I have the "recall" button terminate the workflow I lose out on all the updates I need to happen to the DB, etc. 

Any ideas how to program this?

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