Objectively speaking, she didn't deserve to die.
She is a horrible, abusive woman who deserves to get slapped in the face and thrown out of the Orphanage, but that doesn't mean she should be killed. Many people in the town knows her true identity and they mockingly call her 'the kind' as a running joke.
From her and other children's dialogues, we can derive that while she locks children up in a small den and regularly beats them with belts when they do not comply, she does not use the shackle attached on the wall of the den or sixually abuse them.
Even in today's world, saying that she deserves to die, would put a death mark on millions of people. And consider this: Skyrim is much more cruel world with numerous atrocities than the world we live in. As far as I know, Aventus could have murdered an innocent street beggar or another orphan child to enact the black sacrament. That's what I initially thought when I saw human flesh meat lying about the floor. I expected an option to kill Aventus who, in a rage towards Grelod, overstepped and murdered another person, but for an obvious reason that goes along with invulnerable children, I was forced to kill Grelod with Aventus getting absolutely no consequences for his actions.
I was a little startled by this. It's times of war, and in reality there will be hundreds of new orphans each day. I'm not saying she is spiteful because she is overburdened by her duties of taking care of orphans or anything; it's her nature. Nonetheless, if she, who takes in children(who otherwise would starve to death and get abused even more horribly on streets) and raises funds to feed them, deserves to die for abusing orphans, probably one third of the citizens of Skyrim deserve to die as well.
You wouldn't believe me because you must have encounter many nice NPCs in Skyrim. Take a look at modern day Somalia. War is horrible. Civil war is worse. It wouldn't take a genius to guess that the real condition of living in cities during a civil war is probably a lot worse than how it's depicted in the game. Orphans would probably get stabbed and get striped of clothes by looters if they wander around at night.
I am disappointed that Betheda didn't give an option to bribe city authorities to falsely accuse Grelod of some other crimes, since her abusive behavior doesn't seem to bother guards, then replace her as the head of the orphanage with Constance. Why should I kill her when other citizens don't think she deserves to die?
My character was not even an assassin when I got the quest. I should not have been obliged to kill her in order to complete the quest. I could have stolen another Dark Brotherhood's target instead of doing the bidding of this murderous child.