After the scene with Bourne and that fat guy who killed everybody, he goes to the top of a high-rise building with a sniper rifle. Landy is in her office alone. He calls her says "I hear you're still looking for me."
she says thanks for the tape, your real name is David Webb, your birthdate is 4/15/71. Come in and let's talk about it.
he says "get some rest. You look tired".
at the end of the 2nd movie, you're led to believe that it's over and he's now free to live his life. In the 3rd movie, that conversation takes place in the middle of another investigation to hunt Bourne. That was a turning point because Landy went from being the hunter to helping Bourne.