From the Super Mario Wiki
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During stages, it always appears after playing BYOM or All Wound Up—regardless of whether it appeared before or not—as its purpose is to untangle the player's wrist strap after winding it up in one of those microgames. In the Temple of Form, this microgame appears as a "bonus stage" after playing through all three levels of the two aforementioned microgames. Bungii! can also be played separately in the Remote Control section.