In my experience, Noise Reduction or Noise Removal effects usually let you set a Noise Profile, where you select a few seconds of the sounds you want to get rid of. Then you make a selection of audio you want to apply the effect to. (In theory you could make a profile of a section where music is playing, then apply the effect with that profile onto a section where there is music and dialogue, the frequencies present in the music would be treated as "noise" by the effect). You may get useable results this way, or you go too far you'll end up with audio with that underwater-ish low-bitrate mp3 sound. If it's only a little washy sounding, you can maybe add room noise, new score, or other effects to hide or repair minor audio damage.
I suggested it as the best option because it's free and a good way to dip your toes into the crazy world of repairing/working with "damaged" audio.
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Another interesting option, I had forgotten about before, is phase inversion. How it works: Get a sample of movie audio, like a stereo track from an old dvd with both dialogue and music. Get the official soundtrack for that movie, but make sure it's the same "version" of music that is used in the movie, not alternate takes or remastered editions or anything like that. Place the audio track with the mixed dialogue and music into your audio editor. Place the separate music from the soundtrack with a track that matches what's in the film exactly. Get the position and volume to match. "Invert" the music-only track. You are left with audio minus the music. It's like magic when it works, but it's very difficult to get it right (I've never gotten it to work perfectly the way I described here, it's hard).
This would work with stereo tracks where you can match them up correctly. I don't know what must be done differently for surround sound, as that music is typically mixed differently than what's available on a cd or stereo release.
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If any of these sound interesting, please look deeper into them. I'm in no way an expert, I'm more of an enthusiast.