Hmm... just another thought perhaps (again might be an issue in school?) if you could give her a little nail file and when she gets the urge to rip, she could file them instead? This would also help if she gets sharp edges which is often what starts me biting a nail (I know it's not the same)
does she enjoy story time? is it perhaps a sign of boredom, or concentration? can you give her something to hold so she has something to do with her hands to try and break the habit? one of those squeezy ball things? I've no experience of this, just a random idea. im sure someone else may have some better ideas.
Dd (5) has been tearing her nails on her hands and feet for over a year now. I've tried everything from explaining calmly, to frightening her with Google images of damaged nails to promises of sparkly nail varnish.
She's been in floods of tears when she has ripped her nail too far causing it to bleed. And has vowed and solemnly promised never to do it again. But it's a habit she cannot break.
She's not biting them, she's ripping them off. Often during story time.