The phrase "green band" refers to a type of movie trailer that is suitable for all audiences. It means that the trailer does not contain any inappropriate or offensive content. Full definition
Now, we get the official green band trailer. (movieweb.com)
If you're still not convinced, watch the previous stylish teaser trailer, and the theatrical green band trailer which lays out the story a little more clearly. (slashfilm.com)
The tachometer needle also points to a wide, green band when the engine is off, at a stop or at low speeds. (cnet.com)