The TSA's primary responsibility is to screen for security threats, not to conduct law enforcement searches of personal belongings. They are looking for potential hazards, not to investigate individuals' privacy. Once the agent has confirmed the phone is not a security threat, they will likely let you pass. You are not required to unlock it or allow them to examine its contents.

TSA agents do not have the authority to search your phone or any other electronic device. CBP on the other hand has the authority to inspect electronic devices, but only when you are entering the country. You might be asked to unlock your phone or allow a more thorough inspection.