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I was looking/working through the OWL Online Writing Lab, and it had this sentence, and I was wondering why are there the article "THEs" there when they are being mentioned for the first time?

Is this because the use is triggered/brought about by the context? The paragraph is about a horse bound for a race in a racetrack. The exercise boy, watching the owner's favorite jockey riding the horse he has exercised day after day.

2. Is the following right interpretion of the grammatical situations?

This category has handouts that you can use. (here, the clause "you can have" is not restrictive so the phrase "the handout" is not necessary.)

This category has the handouts that you must use for this evening's shopping spree. (here, the following clause is restrictive so there has to be the article "the" in front of the word "handouts.")
Comments  
Maybe,

If you want something nonrestrictive, you need to put a comma or commas to set off the rest of the sentence. In #2, both sentences are restrictive.

well, in first sentence without " the article " , it means general handouts, that kind of handouts are not in your mind, you've never see them before.

but ths second with the article, you know what the handouts are, you see that before.
Thank you.

I got too loose with the term "restrictive." Sorry. What I meant to say was that it is restrictive in a way that it makes it clear which specific person or thing you are referring to.

This category has handouts that you can use. (It means general handouts and the kinds of handouts that are not in my mind. Thank you.)

How about this?

This category has the handouts that you can use. (In this case, the handouts are not being specified by the following clause/phrase but we are looking at the case of a prior precedence?)
Students: Are you brave enough to let our tutors analyse your pronunciation?
I am not expert but I have something in my mind right now.

Restrictive elements are ESSENTIAL to the sentences in which are the words or noun clauses or phrases, etc.

It seemes to me that " nonrestrictive elements " just add some information a sentence. Even the nonrestritive element has been removed, the setence still can stand itstelf. On the other hands, you definitely cannot delete " restrictive elements on a sentence". Otherwise, the sentence is not clear or does not make sense.