Woman loses her memory in the end [closed]

You might be looking for The Butterfly Effect from 2004 starring Ashton Kutcher and Amy Smart.

It is actually a movie about time travel.

Here the plot from wikipedia explaining her memory "loss":

Growing up, Evan Treborn and his friends, Lenny and siblings Kayleigh and Tommy Miller, suffered many severe psychological traumas that frequently caused Evan to black out. [...]

Seven years later, [...] Evan discovers that when he reads from his adolescent journals, he can travel back in time and redo parts of his past. [...] there are consequences to his revised choices that dramatically alter his present life. [...] Eventually, he realizes that, even though his intentions to fix the past are good, his actions have unforeseen consequences, in which either he or at least one of his friends does not benefit.[...] He ultimately reaches the conclusion that he and his friends might not have good futures as long as he keeps altering the past, and he realizes that he is hurting them rather than helping.

Evan travels back one final time to the day he first met Kayleigh as a child. He intentionally upsets her so that she and Tommy will choose to live with their mother, in a different neighborhood, instead of with their father when they divorce.[...]

Eight years later in New York City, an adult Evan exits an office building and passes by Kayleigh on the street. Though a brief look of recognition passes over both of their faces, they both decide to keep walking.

There are different endings, and the first one in that video corresponds to what you described (it also include the part where he upset the girl):