ask加宾语从句that是否可以省略说明原因

可以，宾语从句的that是可以省略的，跟tell，say一样。
he asked whether he should go back home this winter holiday.
she asked me how to get to the bus station.

这个要分情况
that引导宾语从句时不可省略的九种情况
一、在英式英语中动词add,agree,announce,argue,assume,complain,decide,hold,indicate,insist,intend,learn,promise,point out,remark,suggest,state等之后的宾语从句的引导词that需保留.例如：
I complained that I had been unfairly treated.
二、及物动词后跟有两个或两个以上的宾语从句时,最后一个从句的that不可省略.例如：
I realize that I’m in charge and that everybody accepts my leadership.
三、当动词后跟有复合宾语结构时,it作形式宾语,that从句作真正宾语,引导词that不可省略.例如：
We consider it an honor that we can have the pleasure of serving you.
四、当动词和that从句之间有插入语或者主句的状语时,that不可省略.例如：
The secretary said,pleasantly and sternly,that our thinking was too slow to suit the needs of modern society.
We learned at school that everything we see and touch is matter.
五、当that从句的状语紧跟在that之后时,that不可省略.例如：
They told us that once again the situation was serious.
试比较：They told us once again that the situation was serious.
六、当作宾语的that从句移到句首时,that不可省略.例如：
That she ever said such a thing I simply don’t believe.
七、在简短答语中当that从句单独出现时,that不可省略.例如：
What did he say at the meeting?
That the situation was serious.
八、当that从句中含有一个状语从句,且这个状语从句在主句之前时,that不可省略.例如：
Mr Parker understands that unless he pays back the debt,he’ll have to appear in court.
九、当that从句用作in,but,except等介词的宾语时,that不可省略.例如：
The book is unsatisfactory in that it lacks a good index.