There is nothing I can do.

答案是：不錯，that這個關係代名詞在這句There is nothing (that) I can do中被省略

但我常說給予答案並非難事，但若只知道答案而死記，那麼就容易成為“香港填鴨式教育制度的犧牲品”，所以我們要明白，在甚麼情況下，關係可以被省略，以在我嘗試略略簡述，希望你明白其理，以後遇上，就不會迷惑：

在下列的情形下，可以將關係代名詞省略，尤以口語用法的省略，更為常見

1)限定用法的關係代名詞，為受格的時候（但what例外，即使它是受格，也不可省略）
如：This is the boy (whom or that) I met yesterday. ( )表示可以省略

2)作主格用的關代名詞，於下列數種情形時，也可以省略
a)作補語的時候
如：He is not the man (that) he was when I saw him first.
　　He is not the honest boy (that) he used to be

b)關係代名詞在所引導的there is子句中為主詞的時候
如：I have told you all (that) there is to tell.
　　Please tell me the difference (which) there is between a moth and butterfly.

c) 句首是There’s, Here’s, It’s 等，而先行詞為其主詞的時候
如：There is a man at the door (who) wants to see you.
　　It is not every boy (that) gets a chance like that.

There is nothing I can do. = There is nothing that I can do.
如你所講，呢度係可以有 the，因為佢係由主句（There is nothing）同子句（that I can do）組成，仲係 defining clause（冇comma隔開）。Informal English中經想都減省左中間o既pronoun，如：
He's the man (whom) I want to see.
That's the car (which) I would rob a bank for!
括號中o既字日常用都常省略。

There is nothing I can do.
There is nothing that I can do.
兩種用法都得!

唔係~~~~~~~ 一樣可以啊~~~!