Is the sentence below correct? It has no importance for me what do people think about me.
I agree with the comment. The word "do" in the original sentence is unnecessary and should be removed. Then it sounds alright. The two examples below only need to be changed slightly to sound more natural:
It is of no importance to me what people think about me.
It is not important to me what people think about me.
Using either of these two changes (first change bolded and second change in italics) makes the original sentences sound better.