You, or your producer most likely, have to face a choice: Do you 1) reshoot, 2) do you composite the scene in a way that matches the existing footage (lit room with flat lighting, out of focus background) or 3) do you composite to your ideal background knowing it doesn't match.
Beyond that, it's foundational:
1) Edge control and blending
2) Color correction
3) Motion tracking
No amount of color correction can change the lighting on a 2d element. What increases the problem is that, as humans, we've evolved a very fine sense for light direction, perspective, and so on.