You can build a Rule to create a CTA from something happening in Salesforce. You could either use the Events framework to act as listener for that change and create a CTA when that checkbox changes to False OR you can make the Rule query for Contacts that are false and last modified date of today. The second method would work unless a change was made to a contact that was already false, which you could solve by tracking the history of that field in order to find just contacts that changed from true to false today.

+1 to what John said. While you can build rules to create CTAs on any sort of data changes, the Gainsight Sponsor Tracking feature looks at the LinkedIn public profile data to trigger sponsor change events. 

thanks Dan and John.  So if the active checkbox is unchecked by someone not in CS, we can or cannot use that as a trigger for a CTA?

You can use it as a trigger via Rules Engine.