Is there any way to preserve the exact green color that we desire?
Yeah, you can filter the exact green color you want. However, if you zoom in really close to the intersection between the leaf and the background, the pixels are not the exact green color you want.
@theyComeAndGo Premultiplied alpha gives you exactly the right color. Just consider the example in this slide: if the alpha were 100%, you'd get exactly the same green for the final result as what you started with. Likewise, the alpha-blended (light) green in the frame buffer is the right color; it's just 50% transparent. ;-)