Based upon a close reading of Ray Bradbury's Fahrenheit 451, Montag does not remember where he and Mildred met, any more than Mildred does.
Montag feels extremely distanced from Mildred. As they are in their beds waiting for sleep to overtake them, Montag has a desire to speak to his wife, to connect in some way:
And suddenly she was so strange he couldn't believe he knew her at all.
So he asks Millie how and where they "originally" met.
"I don't know," she said.
He was cold. "Can't you remember?"
"It's been so long."
"Only ten years, that's all, only ten!"
She tries to think, with an "odd little laugh."
He lay massaging his eyes, his brow, and the back of his neck, slowly. He held both hands over his eyes and applied a steady pressure there as if to crush memory into place. It was suddenly more important than any other thing in a lifetime that he know where he had met Mildred.
Montag is trying to "crush memory into place," but it does not say that he has the answer to his question. The reader gets the sense that he is only able to try. The reader can infer that he cannot remember because all of a sudden it is more important than anything else in his "lifetime that he know" where they had met. That he know implies that he is desperate to remember, but cannot. When Mildred says that it doesn't matter, he agrees that it probably does not.
This seems just another reminder for Montag of just how out of touch he has become with the natural world and even his past. In following society's rules, simply one more person who cannot remember that things were ever any different, Montag also becomes aware of how alone he is. He finds that life in their home has been filled with the parlor TVs and the Seashell plugged into Mildred's ear. Even though she does not fully understand what is going on in the televised programs with their "relatives," she is completely satisfied to be further socially and emotionally sedated by the technology that surrounds her each moment of every day.
To Montag, Mildred has become "an unknown, a street face, a newspaper image." He sees a woman who is empty. The memory of Clarisse placing the dandelion under his chin and announcing that he is not in love simply makes him feel worse. A wall has risen between Montag and Mildred, and there seems to be nothing he can do to remove it—especially in that she is not even aware it exists.