First let me say that I am so sorry that this has happened to your mother. I imagine the damage done to her lip must be severe if she's looking at plastic surgery.
This is a tough situation. You're asking what you should do, which seems to indicate that you are as yet undecided about whether or not to re-home your grey. I guess the first thing to determine is whether or not you have a choice in the matter. Are you a minor living with your mom?
If you do decide not to re-home, there are things you can do to prevent something like this from ever happening again. I don't say this in a pointing fingers kind of way, but your bird really shouldn't be allowed to roam the house without supervision. My birds are fully flighted and allowed to fly anywhere in the house they would like (except bathrooms), but I make sure to have eyes on them wherever they go. There is just so much mischief they can get into otherwise.
I also don't know if you grey is typically a biter or if this represents a deviation from the norm. But either way you want to make sure that, in future, she does not have access to a sleeping person. There's no way to know what precipitated the bite. A sudden movement by your mom in her sleep or a shifting sheet could easily have caused a loss of balance that led to the bite. Again, supervision would prevent this. As would keeping the door of a sleeping person closed.
Remember, our birds live in our world, but they are not "born to it" so to speak. Our way of life is not natural for them. As such, we have to adapt our lifestyles around them at least as much as they have to adapt their behavior around us.
My best wishes toward your mother's swift and complete recovery. Please keep us updated.