"It's a good thing I am going away," she said to Gurov. "It's the finger of destiny!" (2.35)
Anna is simply trying to justify she and Gurov's unfortunate circumstance.
"I shall remember you...think of you," she said. "God be with you; be happy. Don't remember evil against me. We are parting forever – it must be so, for we ought never to have met. Well, God be with you." (2.39)
Again, Anna's guilt manifests itself in these ideas of fate, of what must be, of what ought to have been.
The train moved off rapidly, its lights soon vanished from sight, and a minute later there was no sound of it, as though everything had conspired together to end as quickly as possible that sweet delirium, that madness. (2.40)
Notice that Gurov adopts the same fatalistic attitude that Anna did before she left.
Here at the station was already a scent of autumn; it was a cold evening.
"It's time for me to go north," thought Gurov as he left the platform. "High time!" (2.41-2)
Gurov's mood is very much a product of his environment; this is why he feels the need to change locations once Anna leaves.
What savage manners, what people! What senseless nights, what uninteresting, uneventful days! The rage for card-playing, the gluttony, the drunkenness, the continual talk always about the same thing. Useless pursuits and conversations always about the same things absorb the better part of one's time, the better part of one's strength, and in the end there is left a life groveling and curtailed, worthless and trivial, and there is no escaping or getting away from it – just as though one were in a madhouse or a prison. (3.12)
There's something fatalistic in this passage, as though Gurov has no control over the circumstances of his life.
He was sick of his children, sick of the bank; he had no desire to go anywhere or to talk of anything. (3.13)
Anna has completely changed the course of Gurov's life – he's unable to return to normalcy after their affair.
He considered: to-day was a holiday, and the husband would probably be at home. And in any case it would be tactless to go into the house and upset her. If he were to send her a note it might fall into her husband's hands, and then it might ruin everything. The best thing was to trust to chance. (3.18)
But as Gurov soon finds, trusting to chance isn't possible. Part of his transformation in "Lady with the Dog" is about actively pursuing what he wants – in this case, Anna.
He walked up and down, and loathed the grey fence more and more, and by now he thought irritably that Anna Sergeyevna had forgotten him, and was perhaps already amusing herself with some one else, and that that was very natural in a young woman who had nothing to look at from morning till night but that confounded fence. (3.19)
Metaphor much? Anna is hemmed in by her fence the same way she and Gurov are each hemmed in by their marriages.