Which maneuver is not permitted by ATP for checking landing gear configuration during unsafe gear indications?

The correct answer is determined by understanding the regulations and operational safety procedures for checking landing gear configuration during instances of unsafe gear indications. Tower flybys are not permitted as a means of checking landing gear configuration because this maneuver can pose significant risks to safety. A tower flyby involves flying close to the control tower, which could obstruct proper inspection of the landing gear and mislead both the flight crew and ground personnel regarding the aircraft's configuration.

In contrast, touch-and-goes, go-arounds, and touch-and-stops are operational maneuvers that may allow for safer evaluations of the landing gear status while still maintaining optimal control over the aircraft and ensuring safety protocols are followed. These alternatives provide an opportunity for the crew to verify the configuration without the risks associated with a flyby, where altitude and airspeed management is critical, and the focus might be divided.

In conclusion, the safety implications of the maneuver, along with regulatory standards within aviation, dictate that tower flybys are not permitted for checking landing gear configuration under unsafe gear indications, making it the correct answer.