we have been informed that he had done ( ) visits were essential by eleven o'clock last night .
that 在这里引导宾语成句(he had done ( ) visits were essential by eleven o'clock last night .)
he 做主语 had done 做谓语 ,句子中有were essential(系表结构)所以
had done后面接宾语从句,宾语从句就需要引导词
所以答案就是 what