It's our duty (to give good service to customers)

It's + 名词/形容词+ to do something是一种句型.
it是形式主语,to do something是真正的主语或叫逻辑主语.
之所以用形式主语it是因为to do something比is后面的表语长多了,那就显得头重脚轻,因此就使用形式主语it替换不定式做主语,而把真正的主语不定式后置(后置后就是逻辑主语了),使得句子平衡.
It(形式主语) is(联系动词) our duty(表语) (to give good service to customers)(逻辑主语).
再比如：
It is good to do exercise.(=To do exercise is good.)
It is a pity to miss the film.(=To miss the film is a pity.)

duty是宾语，to give good service to customers 是duty的修饰语，所以是宾语补足语。be one's duty to do是个固定搭配，所以得用to