pushdown wh-element
You can do whatever you think is right.
The Comprehensive Grammar of the English Language (查 pushdown wh-element)
The Cambridge Grammar of the English Language
Longman Grammar of Spoken and Written English
The Comprehensive Grammar of the English Language 第1050頁 (pdf, 531)
[d] If the subject of the that-clause is a pushdown wh-element (cf.11.18) and is therefore moved to the front of the superordinate clause, the subordinator that must be omitted, perhaps to prevent that being initially misinterpreted as subject of the following verb:
Who did she hope would be the winner? [1]Contrast [1b] with [1] and [1a]:
*Who did she hope that would be the winner? [1a]
They pointed out the damage which they supposed had been done by last night's storm. [2]
*They pointed out the damage which they supposed that had been done by last night's storm. [2a]
Who did she hope (that) that would be? [1b]In [1b], the second that is indeed the subject of the that-clause; who is the subject complement and therefore the subordinator that may be optionally retained, the presence of a subject that before the verb preventing misinterpretation.
Here are several other examples of optional that when the wh-element is not the subject and hence a subject appears before the verb in the that-clause:
Who do you expect (that) they have chosen?
She told me how she thought (that) the machine worked.
They mentioned the name of the men (who) they knew (that) you had spoken to.
parenthetical clause
who they say
Studies in Grammar - Page 115
books.google.com/books?id=jdZEAAAAIAAJ
Mabel Clare Hermans - 1924 - Snippet view - More editions
.... In this sentence, "He is the man who they say will be elected", we see that the main thought is "He is the man who will be elected." In addition there is the clause, "they say," which has been inserted and is not dependent upon the independent clause. In other words, it is neither an independent clause nor a dependent clause. It has been thrown into the sentence and is called a parenthetical clause. The relation of the parenthetical clause to the rest of the sentence is shown in this way:
You will see that the complex sentence is complete without these words, but since they are expressed, we ...
Who Versus Whom--Advanced (link 被移除了)