What's the underlying grammatical structure of this sentence with three instances of "it" and two of "being"?
The parenthetical participle clause
- it being immaterial that the words are not in English
is the result of Extraposition (with dummy it inserted) on the parenthetical participle clause
- that the words are not in English being immaterial
Extraposition is very common in English when the subject of a short verb phrase (like being immaterial) is long and syntactically complex (like that the words are not in English). It moves the heavy material to the end, where it's easier to parse in a right-branching language like English, and leaves a harmless little one syllable marker that leads right into the auxiliary verb, which is what English prefers.
If you exaggerate these dimensions, you see how useful it is. Contrast
- That I had to stand in line for over an hour yesterday is too bad.
versus the extraposed version
- It's too bad that I had to stand in line for over an hour yesterday.
Oh, and as for the two beings, the first is simply the progressive construction operating on the passive be presented, producing is being presented, a tensed main verb chain. The second one is a non-finite equivalent of a tensed subordinate clause. In this case, something like
- since it is immaterial that the words are not in English
with the same extraposed clause. Unlike the first, this being is not tensed, since it's a participle.
Your highlighted text is what is called a nominative absolute, which is used to describe the subject of the main clause, the "direct quotation," but is essentially a separate clause in its own right, and has almost no bearing on the first clause - in other words, it is completely parenthetical. If reworded, it could stand as a separate sentence, as "It is immaterial that the words [of the direct quotation] are not in English."
The "it" you're questioning is the subject of this absolute, so no, it cannot be deleted and maintain the integrity of the sentence.