B.B.
My son also did this. He has an outie, and it was definitely a comfort thing for him. When he picked it raw, I put him in a onesie so he couldn't get to it, but that probably won't work with a 3 year old. My son has since moved on to his nipples. It's a self soothing thing for him, that he does when he's tired or upset. Have you tried giving her something else to play with? Tell her if she's tired or upset, to play with a special blankie or stuffed animal instead. I thought it was just my kid who did this! Good to know he's not the only one!