Symbolism, Imagery, Allegory
The check, or cheque, to use Poe's spelling, that G— writes to Dupin (86-87) symbolically shows that the letter has become an item for sale in the marketplace. We don't know exactly what it was before it was turned into a marketable item, but the most obvious answer is that it was a love letter of some sort, one side of a private and intimate correspondence.
Neither Dupin, D—, G—, nor the narrator seem to find this at all touching or even particularly scandalous. They value the letter because, so long as the letter is out of the lady's hands, it can provide money, power, and influence to whomever holds it.