I want to automatically get the circled stuff in the thin (small) rectangle area. Unfortunately, grabcut does not work well, i.e., often fails. Therefore, I am searching for a solution for this.
Depending on what your ultimate goal is, you could draw the bounding box and capture the coordinates write some code to crop the image to just the ROI. That may remove enough of background for your needs, or you can try the Grabcut from that point on the cropped image... although I see the challenge in low contrast.