Inverse a PIL.Image.QUAD transform operation to overlay a section of an image back onto the original image

Given the code attached, it extracts and aligns a head from an image. I want to modify this extracted head and then paste it back onto the original image. The code below needs to perform an inverse of the PIL.Image.QUAD transform. Also attached is the test image. I do not want the code modified to change the shape, size or anything else.