Some interesting words have been said concerning the use of style. However, the original sentence became even more interesting in the process.
One of my biggest complaints about grammar books is the tradition of using simplistic examples. Then when I have to figure out a complex sentence the examples don't appear to apply at all.
Which brings me to the/an for ESL speakers. There are millions of explanations of how articles apply to a word, but very rarely is it shown how it can affect an entire sentence. However, from post 2 onward, it became obvious that the example sentence of Coco's is an excellent example of this potential misunderstanding.
Essentially, maybe it's a better idea for ESL speakers to go ahead and leave the "that" and such in place when in doubt. It doesn't really hurt anything, and it can help prevent any confusion if they accidentally misuse an article.
The teacher brings in an old pen that Franklin Delano Roosevelt used during his (the teacher's) Presidency.
Usually, context will clarify a misused article, but when it doesn't, a misused article really grates on a native speaker's ears. So I'll make another sentence with the same construction to demonstrate this.
The teacher brings in an old dog that Ralf found outside the school.
Nothing wrong with this sentence. However, Ralf can be both a Dog's name and a Person's so there is potential for confusion. "That" clarifies that Ralf is a Person's name regardless of the article used. Now let's drop "that."
The teacher brings in an old dog Ralf found outside the school.
This sentence means the same thing, because the article used is "an" we know that "Ralf" does not describe the dog.
The teacher brings in the old dog Ralf, found outside the school.
Changing "an" to "the" completely transforms the sentence without "that". Now Ralf describes the dog and, apparently, the tearcher found the dog, where before it was Ralf. Also, this sentence pattern no longer stands alone very well, but it can be found within a paragraph, where sentence patterns are modified to fit a desired rhythm. In fact, the last example would probably continue on to say something more.
The teacher brings in the old dog Ralf, found outside the school, it took 3 weeks of care before the dog was ready meet new people again.