Probably a liability related decision...I expect it's not unlike why Vega become M. Bison in Street Fighter II, why scads of names got changed in JoJo's Bizarre Adventure, etc. People can nerdrage about this if they wish, but it's nice to live one's life without getting sued. It's especially nice to not get sued by the RIAA, a group of people who have raised soullessness to an art form.
Even so, the Japanese version had an alternate subtitle: "Tengoku no Tobira", or "Door to Heaven" which is also relevant to the movie's plot in a way that "The Movie" is not (though it does, admittedly, lose the music-related pun).
In fact, every episode of the show actually had both an English title and a Japanese title (even in the untranslated Japanese version). For many of them, the Japanese title was just the English title in katakana, but not all of them. For example, "Toys in the Attic" was also "Yamiyo no Hevi Rokku" ("Heavy Rock of the Dark Night"), and Pierrot Le Fou had a Japanese title of ""Dōkeshi no Chinkonka" ("Requiem for a Clown"). The movie did the same thing.
So there's no reason they couldn't have called it "Cowboy Bebop: The Door To Heaven". Calling it "The Movie" seems just too on-the-nose, like calling the next Avengers film "Avengers 2: The Movie" instead of "Avengers 2: Age of Ultron."
(And it's not "nerdrage" to dislike or disagree with something. If a simple statement like "I think 'Knockin' on Heaven's Door' or even 'Door to Heaven' is a better subtitle than 'The Movie'" is something you interpret as rage, then I wonder what you call actual screaming rage)