How to participants opt out of receiving text messages? Can we see when they do?

Any participant replying to a message with STOP will be opted out from receiving additional text messages from you. This is a requirement of the mobile carriers. 

If they've done so accidentally, they can opt back in by texting START to your number. You can manually update their opt-in status via their participant profile.

An Opt-Out report is available in Basic, Plus and Pro Plans.