Your THM-4T65E transmission is a four speed auto with a lock-up torque converter clutch (TCC) that works on 2nd, 3rd and 4th gears. When you lift your foot at speed, the engine is driven by the rear wheels and the control unit shuts off the injector pump. See:
4T65E Transmission Info
This is a very reliable and mileage-efficient transmission. However, like ALL automatics, you can damage this transmission by coasting in neutral, regardless of whether the engine is off or on, because it is lubricated by a front engine-driven pump that requires higher engine rpms at speed. Therefore if you coast at speed in neutral at idle, the pump will not be receiving sufficient rpms from the engine to properly lubricate the transmission.
I know you didn't say you were coasting in neutral, but I have noticed that some people on other threads were confused by this subject so I thought I should mention it.