Observation: "Take back" is used in impolite speech, while "Bring back" is used in polite speech. Is there any basis to this?

Solution 1:

Observation: “Take back” is used in impolite speech, while “Bring back” is used in polite speech. Is there any basis to this?

None whatsoever.

Both are the imperative form.

To take usually implies away from the speaker. To bring usually implies towards the speaker.