Let's play around here. Green is often associated with nature, and Dupin definitely thinks G—'s way of searching for the letter is highly unnatural. Plus, G— and his force sound more like machines than men with their "accurate rules" and needles and microsopes and diving "entire surface[s] into compartments."
Dupin's approach, in contrast, involves intuition, and invention, like asking himself "how and where would I hide the letter if I were D—?" And it takes green spectacles to help him answer that question.
But, aside from the possible implications of the colors, the tinted lenses symbolize Dupin's willingness to explore multiple versions of reality. He puts the tinted glasses on to see the world in a new light and to look through other eyes—like D—'s.