GMAT Sentence Correction (SC) | Re: Priya and her barking toy robot dog

Sorry I am still confused I am stuying on the Manhattan SC guide and about THIS,THAT,THOSE,THESE it says te following:
-They cannot take place of a noun unless they indicate a ''new copy'' of the antecedent: ''The money spent by the parents is less that that spent by her childeren.
-they must be used as an adjective referring to nouns
In answer C it seems that ''that'' is reffering to dogs, so why it is uncorrect?
Finally, to evaluate if a sentence is independent I should eliminate everything