If this is truly your text, it seems to be a misprint.
Quotation marks are used for reports of direct speech, that is, reports which attribute specific words to someone. For example,
- Tom: Flies like honey.
- Mike: Tom said "Flies like honey." [Direct speech]
Quotation marks are not used for indirect speech. Further, using a 'that' is an optional way to introduce the clause that paraphrases what the person being quoted said. These are called content clauses or that-clauses. For example:
- Tom: Flies like honey.
- Mike: Tom said (that) flies like honey. [Indirect speech]
"That a teddy bear from 1996 is not an antique" is NOT a grammatical sentence. The 'that' is licensed by the fact that this is supposed to be indirect speech. As such, there should be no quotation marks in the sentence. You textbook should probably read:
Then Tom said that a teddy bear from 1996 is not an antique.