In the story, the narrator includes the reference to the tear gas to make a point about his self-image: as an immigrant living in an American suburb of New Jersey, the narrator is ever aware of his "foreignness" to most people. Additionally, he believes that this "foreignness" often gets in the way of his having a successful date, especially with a white American girl. Essentially, the narrator feels self-conscious about his racial and national heritage.
He references the tear gas used during the American invasion of the Dominican Republic but admits that he would never divulge this part of his heritage to a white girl. So, the reference is for us readers rather than for the white girls he hopes to impress. The text tells us that he will only mention the tear gas as a factor in some fantastic story about "the loco who'd been storing canisters of tear gas in his basement for years, [and] how one day the canisters cracked and the whole neighborhood got a dose of the military-strength stuff." However, he will not mention why and how his mother easily recognizes the smell of tear gas.
The narrator sees the story of his neighbor as an exciting story that will impress a white girl, and that's all that matters to him. However, he will stop short of alluding to any past conflict between the United States and the Dominican Republic (where he or his family are originally from.) He fears that doing so will alert the girl to his "foreignness" and so, destroy his chances of gaining sexual fulfillment. He admits, "The white ones are the ones you want the most, aren't they...."
So, the historical background behind the tear gas reference is for us readers. The narrator is telling us how he really feels about himself and how much he fears his "foreignness" will get in the way of him successfully having relations with white girls.