We've been using an SSM Parameter to track the existence of review apps, but for folks with lots of review apps, that is pretty slow to search through all of them. We also seem to have an issue where the data in the parameter isn't always getting synced properly.
It would be easier to find all the cloudformation stacks that match apppack-reviewapp-{name}\d+. I don't recall offhand if the individual app users have permissions to list Cfn stacks though.
This issue also applies to the web dashboard.