"because of diminishing" is wrong, out B and E.
"respiratory system in dealing" is unidiomatic, out C.
We are down to A and D:
A. an especially serious pollutant because it diminishes the respiratory system's ability to deal
D. a specially serious pollutant because it diminishes the capability of the respiratory system to deal
The differences are:
1)"an especially serious pollutant" VS "a specially serious pollutant"
2)"respiratory system's ability" VS "the capability of the respiratory system"

IMO A
because "especially" is better in this contest than "specially"
and because the "ability to deal" sounds better than "the capability (...) to deal"

IMO A. we should use ESPECIALLY and not specially.
ESPECIALLY means in particular
SPECIALLY means overly special.
so that leaves D and E out.
DIMISHES X's ability TO DO SOMETHING is better and concise.
we will prefer dimishes ability to do something versus "Because of dimishing".
Hence A.

Good thoughts, all - and if I can add one big-picture takeaway here:

One way to think about the difference between "because it diminishes" and "because of diminishing" is that "it diminishes" is very specific and clear. Sulfur dioxide is what diminishes the respiratory system's ability. "Because of diminishing" doesn't directly attribute Sulfur dioxide as the cause of that lessened ability - in that case the sentence is unclear as to where that diminished ability comes from. Is sulfur a problem because it, itself, creates the problem? Or is sulfur a problem in conjunction with the already-being-diminished ability?

If you're between a couple of choices and can't quite tell the difference, ask whether one of the choices gives a clearer, more direct meaning. And if it does, make sure that it's a logical meaning; if it is, that's usually the correct choice. The GMAT tests a lot of clarity-of-meaning / accuracy-of-meaning sentences, and this is a pretty good example here.

IMO A