Like I said earlier (maybe not so well :innocent

is that perverts have a way of recognizing each other and associating together. Grampa was an RSO. My instinct is that he "recognized" something similar in MP.
Yes, neither grampa or any of the other charmers in that park murdered Aliahna, miraculously, IMO. But Aliahna was murdered by someone who was there because he was associating with that riff raff. Even if it wasn't because he and grampa had things in common, hiding out with RSOs who have limited choices as to who they can room with, may have seemed like a good option for the fugitive MP. Either way, I connect grampa's sex offender history with what happened to Aliahna.