根据张道真《英语语法大全》第1478节的分析，be surprised that 中的 that 是引导宾语从句。

张道真《英语语法大全》给出的相关说明是：一个系动词和一个表示精神作用的形容词 (或过去分词) 可构成动词短语，在语法上相当于一个及物动词，后面可跟一个由that引起的从句作宾语。如：

I am sure(=believe) that he is at home.

He was afraid(=feared) that he would fail.

I am notdoubtful (=don’t doubt) that he will succeed.

He is aware(=knows) that I cannot help him.

I am glad (=rejoice)that the war is over.

He becameangry that you made the same mistake.

I madecertain (or sure) the door was closed.

He remains(or keeps) confident that he will win.

He is deeplyinterested that I’ll study in France.

He appeared(or seemed) surprised that I said “no”.

He felt (orgrew) worried that you didn’t write.