Might I had that the bottom of the stone is very dirty sothat may be causing some issues in its clarity
Doesn't make any difference with a diamond. One of the most interesting characteristics of a diamond is it's high refractivity which returns almost all the light that enters it out through the crown. This is what creates its dazzling sparkle.
If you can "see straight to the bottom" of a diamond, it's extremely unlikely to be a diamond.
Likewise, dirt on the outside of the pavilion (the bottom section of a diamond) can't be seen from the crown because you can't see THROUGH a diamond, either. All part of that refractivity thingy...
Now I suppose it's POSSIBLE to see these things in an extremely poorly cut diamond, but that's also unlikely since I suspect that any cutter that botched a diamond that bad would probably recut it into a smaller diamond rather than bear such shame
, though one of the "4 C"s is "cut" since it does effect its refractivity.
FWIW, the other 3 Cs are carat, color and clarity.
Should I pull back the posts and remove the stone to clean it?
I wouldn't advise it for 2 reasons:
First is that the posts are relatively fragile and are difficult to pry back without stressing the posts to the point of breaking or weakening them. Trying to remount the stone after cleaning can also be problematic since there shouldn't be ANY play in any of the 4 posts.
But more importantly is that it's unnecessary for precious gems.
Precious gems are mounted in such a way that all of its surfaces are exposed to light. the only part physically being touched by the ring are the mounting posts around the girdle.
This also means that the entire gem is exposed to cleaning procedures and materials. A toothbrush usually works well, but for obstinate dirt you might have a jeweler clean it ultrasonically.