syntax

If you omit 'they' the sentence is meaningless.

No, you cannot eliminate "they" from that sentence. I don't see this as a matter of syntax, however.

In that sentence, you need it. You do not need the quotation marks, though I'm sure you just added them to clarify the question.

thanks for your answer, but of course, this is a problem of syntax given that all the sentences have a word order. As you can see if I eliminate the pronoun "they" I am going to distort the meaning!

No, you're mistaken. I have something else to do right now, but i'll come back in a few minutes to show you what i mean.

"I miss your reactions in public although I always said to you that they embarrassed me."

(You need to punctuate your sentences properly--that sentenced needed a period at the end.)

It is not the order of the words, it isnot the arrangement of the words that would be the problem if you eliminated "they" from the sentence. The problem would be the lack of a referent, the lack of an explanation of what embarrassed you.

Although i always said that they embarrassed me, i miss your reactions in public.

The word order is changed, but the meaning is the same. You could also use the passive voice and change the pronoun from subjective to objective and say the same thing.

I miss your reactions in public, although i always said that i was embarrassed by them.

Although i always said that i was embarrassed by them, i miss your reactions in public.

Do you see? It's not the word order, nor the sentence structure, it's a matter of having a referent to what embarrassed you.

If you eliminate the pronoun "they" you are going to eliminate the meaning!

"Syntax refers to sentence structure; it’s the order of the words in a sentence that makes it understandable to native English speakers"

I am not talking about the sequencing of subject, verb, and object, I am talking about the absence of a word. If I eliminate the word "they", it can be generate problems related to interpretation.

let me know your argument! It is good to know other views!

I got it!You are right when you say that it is a problem about reference, so it is related to semantics and not to syntax!
Thanks setanta for the explanation!

Those damn s words!

You're welcome, and you're absolutely right, it is a matter of semantics, in this case a matter of reference.

Those damned "s" words!