Any idea on how to make the white region the same color as the light brown background without bothering the axis, or curves?
If the graph is a vector image do as already said by others: Explode it and remove the white background object. If it happens to be a bitmap image PNG JPG, TIF etc.. and cannot be disassembled, then use blending modes. Multiply is already suggested. It fades completely the white and black stays intact. Unfortunately other colors are mixed with the non-white background. That can be OK if the other graph colors are dark and the background is quite light as it's now.
Darken is another blending mode which works if the graph colors are all darker than the background. It's used in the next image. A piece of your background is stretched below the graph:
As you see, the blue and black stay both intact. If the graph has also light colors you must darken them. To do it for a bitmap image use GIMP.