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She doesn't remember the kiss, but he does. It's etched into his memory with fire and lightning. It tingles on his lips every time he looks at her, even before he really knows who he is this time. That doesn't matter. She matters. She matters enough that he—the old him—died to save her, fought tooth and nail for a few more words, a few more seconds just to talk with her.
He was so sad to leave her, he remembers. So afraid. But that's over, now. When Rose smiles at him and grabs his hand, he knows it's the two of them against the universe. They'll run so fast and so far that nothing will ever stop them.
He tries not to think about how long "ever" can really be with a little mayfly human. It's easier when she takes his hand and grins, that special grin she seems to keep just for him. Instead he thinks about tomorrow, about what new wonders he'll show her next.
And at night, when she's asleep and the only sound is the quiet hum of the Tardis, he remembers the kiss.