yea it might help if we can see your source image. it looks like its way too dark around the edges(ie under lit) but without seeing the original its hard to say. Hyperloop is correct that capturing source for greenscreen also has quite of a bit of technique to get something useable. Ie, the colored blanket in that example image almost certainly was sold as a special chroma key blanket that matched the background exactly in color.
That said, the “unpremultiply” trick is kind of designed to help your situation I believe. Its where you divide the original image by the final opacity. what that does is kind of normalize the colors around the edges so they get brighter at exactly the rate your alpha fades to black. The catch is that if your texture really is super dark there, that operation may just bring out some nasty random color pixel artifacts.