So, all you role players who want to find some way to destroy the DB but are having problems with justifying killing Grelod, take the following steps:
1) Do not talk to the Arentino kid before visiting the orphanage in Riften.
2) Once in the Orphanage, throw a tomato at her. Who, after all, could claim that was murder?
3) Now go talk to the Arentino kid.
You did not kill Grelod to fulfill some kid's revenge fantasies. And if it came up in court, no jury would ever blame you for throwing a tomato at the old bat.