The thing is 不是插入语,The thing 是第二句的主语,is 是系动词,I forget to bring my homework 是表语从句,它和系动词一起构成谓语.
换成 It is 还可以.
不可以换成This is,因为this用来启下；可以用that is,因为that用于承上.
换成 which is 可以,但是两句合并成一句,后面那句成了定语从句：
There is something I need to tell you,sir,which is (that) I forget to bring my homework.不过更像书面语.