What does tensorflow nonmaximum suppression function's argument "score" do to this function?
The scores argument decides the sorting order. The method tf.image.non_max_suppression goes through (greedily, so all input entries are covered) input bounding boxes in order decided by this scores argument, selects only those bounding boxes from them which are not overlapping (more than iou_threshold) with boxes already selected.

NMS first look at bottom right coordinate and sort according to it and calculate IoU...

This is not correct, can you site any resource which made you think this way?
I read the document about the function and I understood how NMS works. What I'm not clear is scores argument to this function. I think NMS first look at bottom right coordinate and sort according to it and calculate IoU then discard some boxes which have IoU greater than the threshold that you set. In this theory scores argument does absolutely nothing and the document doesn't tell much about scores arguments. I want to know how the argument affect the function. Thank you.