This encounter occurs in Chapter VI when Tom drops in at Gatsby's house on a Sunday afternoon, along with his two riding partners. Nick is there visiting Gatsby when the three unexpected visitors arrive. It is an uncomfortable situation for both Nick and Gatsby, since Gatsby has recently resumed his love affair with Daisy, as Nick well knows since he arranged their reunion. Tom, however, gives no sign that he recognizes Gatsby or has any knowledge of him.
At first Gatsby scurries about, acting as the gracious host. Then, quite suddenly, acting on "an irresistible impulse," Gatsby tells Tom they have met before, referring to an earlier incident when Gatsby actually had disappeared to avoid Nick's introducing him to Tom at lunch. Tom pretends to remember, but clearly he does not. Gatsby persists until Tom does remember that Gatsby had been with Nick. When Tom does acknowledge remembering him, Gatsby says, "I know your wife." He says this "almost aggressively."
This exchange begins the power struggle between Tom and Gatsby over Daisy. Gatsby seems to be initiating it, setting in motion the events that must occur before he and Daisy can be married. Also, in a psychological sense, Gatsby is being aggressive and dominant. He forces Tom first to acknowledge him and then to pay attention to who he is and what he has to say. Gatsby will not be ignored.