Grandpa likely noticed there were missing rounds. And certainly he noticed that there's a dead guy in the trailer park when the police showed up and started asking questions.
Maybe grandpa is an alcoholic who wondered if he killed the guy during a blackout? 100% speculation on my part.
Or the kid came back and was noticeably different, or showed too much interest in the case, or something else clued him in, and when he checked the gun he saw it had been fired.
Chances are the family knew something was up with the kid. Kitchen knives could have been disappearing and turning up under his bed he could have been caught torturing animals or hurting relatives. He wasn’t this screwed up and nobody knew.