The journalist stated she had gotten that piece of info from a reputable source which answer correctly describes the bolded word

If your options are: 

The word “that” is an adjective describing which one.
The word “that” is an adverb describing where.
The word “that” is an adverb describing to what extent.
The word “that” is an adjective describing what kind.

The correct answer is A. The word “that” is an adjective describing which one. It is an adjective because it goes with a noun and provides an additional information about it - in this case, it describes which piece of info, referring to the one that was already mentioned previously in the text. It doesn't describe the kind of information - we don't see that here. It can't be an adverb because describe verbs.