Moot point is the standard phrase, not mute point. The confusion is common because the two words sound similar in some accents, but they mean different things.
Moot refers to something open to debate or no longer worth deciding because the situation has changed. In modern everyday use, people often mean the second sense. For example: The refund issue became moot after the company returned the money.
Mute means silent, unable to speak, or not expressed. It does not fit this phrase. You can say the TV was on mute or he gave a mute response, but not that is a mute point if you mean the issue no longer matters.
- Correct: This argument is a moot point.
- Correct: Please mute your microphone.
- Incorrect for this meaning: That is a mute point.
If you mean debatable or no longer worth deciding, choose moot.