In The Diary of Anne Frank, Peter's explanation for removing his yellow star is that he no longer wants to wear something which identifies him for the Nazis, that for him it has become almost a badge of shame.  He tears it off with emotion because he is now in hiding and doesn't have to be seen with this symbol of Jewishness which the Nazis have turned into a symbol of hate.  Anne sees the other side of wearing the Jewish star; the star has long been a positive Jewish symbol which she cannot treat as Peter does.  The irony of the star is that the Nazis used a well known Jewish religious symbol and turned it into a terrifying badge to hide.