she was taking 是个定语从句,修饰前面的先行词 risk.由于risk 做take的宾语（词组take a risk:冒险）,因此其引导词that或which可省略.意思是“她冒的风险”.
而 when...后面的内容则做整个句子的时间状语.
she 指的就是Mrs.Anne Sterling
本句未省略引导词词前应该是这样的：
Mrs.Anne Sterling did not think of the risk (that / which) she was taking when...
句子意思是：当.的时候,安娜斯特林女士没有想到（考虑到）她所冒的风险.