We created another picklist option for the Status of a Task called "Closed - No Action". However, when you choose this status, the task is not closed out, but remains open. I am sure I am missing a simple setting here somewhere but cannot seem to find it.
If task mapping is configured (see article) and you're just looking to have to CTA or Task be marked off when status is set to "Closed - No Action"– then I'm pretty sure you just have to update the Category in Call to action status.
You can find the settings by going to Administration > Workflow > Calls to Action > Call to action status. I think if you select Closed Won or Close Lost under Category for the "Closed - No Action" status, a CTA or Task will be marked off when this is set as the task status in Cockpit.