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.
【结构分析】
【主干成分】主干为but引导的并列句：It is fair to criticize and question the mechanism,but it is the prize-givers’ money。
【修饰成分】of research介词短语作后置定语，修饰culture；2）to do with不定式作后置定语修饰前面的名词money；3）as they please为方式状语从句，修饰动作 do with。
【参考译文】
批评或质疑奖项机制是合理的，毕竟这就是科学领域的文化，但是奖项设立者是有权按照自己的意愿处理这笔钱的。