It is fair to criticize and question the mechanism — that is the culture of research, after all — but it is the prize-givers’ money to do with as they please.
【結構分析】
【主干成分】主干為but引導的并列句：It is fair to criticize and question the mechanism,but it is the prize-givers’ money。
【修飾成分】of research介詞短語作后置定語，修飾culture；2）to do with不定式作后置定語修飾前面的名詞money；3）as they please為方式狀語從句，修飾動作 do with。
【參考譯文】
批評或質疑獎項機制是合理的，畢竟這就是科學領域的文化，但是獎項設立者是有權按照自己的意愿處理這筆錢的。