I don't know why everything has to make perfect sense all the sudden. We don't even know why they skin people to begin with.
It's what they do, it shouldn't be missing from the movies. People still criticise AvP-R for the skinned body, granted, for a cleanup mission it doesn't make much sense, but i always saw it as a "f**king mission... come on, just one time i'll have me some fun" kinda thing from Wolf.
Remember, Predators are having fun killing people, up to the point where they do stupid things, basically in every movie. If they would just rationally kill people and fly home no one would have ever survived the movies.
In the end of the day, it didn't compromise his mission at all. They didn't find the skinned body and yelled "Alien!".
Guys, from all the things that have to make sense in order to make a good movie, none of it is a skinned body hanging from a tree.