There are a lot of blank shell casings, M60 belt links, etc. laying around the Hawk Mountain area. I never saw MRE wrappers or any such thing there when I hiked through, but things may have changed.
OPFOR (Opposing Forces) may be leaving sign intentionally for Ranger trainees to follow as well.
Empty shell casings can be a PITA to police up and carry. They are quite heavy and make a LOT of noise.
Tactically, once you have made contact and gotten into a firefight, you are no longer covert. Whether you leave your brass and such behind or not isn't going to make much difference. If you were fighting defensively, trying to break contact, you aren't going to waste time picking up your brass, its stays where it lays.
So depending upon the nature of the training exercise, it may be likely that expended brass, links, etc. would be left behind. Also a night engagement is going to make it impossible to do anything like a complete job of picking up, and a LOT of Ranger exercises take place at night.