The caloric deficit will be compensated by fat burning again, so, let's consider another 350 kcal from fat.
This is not what happens. Your caloric deficit was generated by the brisk walk. If you were to eat an additional 500 calories, then the fat/energy burned during the brisk walk will be replenished. At the end of the day your calories burned / fat ...
The basic tenet of fat loss is to be in a caloric deficit.
If you burn more than what you eat then you will, barring unusual circumstances, lose weight over time - this is a marathon, not a sprint.
One thing to pay attention though here is that to avoid losing muscle while on a caloric deficit you need to exercise the muscles too and eat enough protein.