https://i.imgur.com/ClKyPUJ.gifv
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.
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.
who they say