The trapper has a very small part in the story. Basically, his purpose is to bring Shamhat into the wilderness, thus setting in motion the chain of events that makes Enkidu become human and leads to his becoming friends with Gilgamesh. In fact, as soon as he brings Shamhat back to the watering hole, he disappears from the story almost completely. The only time we hear about him again is when Enkidu is on his deathbed in Tablet 7, and is cursing the people who made him become human (the trapper and Shamhat).
On that occasion, the god Shamash steps in to talk Enkidu out of cursing Shamhat, but he doesn't say a peep in defense of the trapper. What do you make of this? We don't really know the answer, though it does seem like the trapper has a pretty nasty personality. After all, what did Enkidu ever do to him? Even though the trapper claims that Enkidu was freeing animals from his traps, we never see him do it.
From what the story shows us, Enkidu just shows up at the same watering hole, and the trapper doesn't like the looks of him.