The Moon never loops back on itself as it travels around the Sun. Its path is nearly a circle with a slight ripple in it, always curving the same way.

The Sun pulls on the Moon about twice as hard as Earth does. Draw the Moon's actual track around the Sun and you don't get loops; you get a nearly circular path with a gentle 13-times-a-year ripple. In the Sun's frame, Earth and Moon look less like a planet and satellite and more like two bodies orbiting together.