答案是C.
1.如果不看E答案的前半部分about notifying students of their missing documents required for graduation,只看 as they are responsible的话：
they 的指代一般应该没问题.即如果E答案换成to notify students of missing documents required for graduation; however, they are responsible的话也是不妥的 应加上for it .
2.原句with notification to students of missing documents required for graduation; however, it being their responsibility 如果改为with notification to students of missing documents required for graduation; however, it is their responsibility的话 我认为是正确的.
不过这里with介词短语作原因状语或方式状语 与 to不定式 作目的状语 意思上是有区别的