I got 3 new chicks a few days ago. One of them pecks everything. She will NOT stop pecking at the waterer. It is so weird. I've never seen a chick do it.
It's just their way of exploring their world. Give them more things to explore -- including the outdoors, as soon as you dare, for short periods at first. Mama hens take their chicks out to forage, scratch and peck, at 2 or 3 days old.
Is she seeing her reflection in it? My silly girls are constantly pecking at their reflections in the glass waterer, and the sides of the plastic brooder.
You might try putting a piece of sod in the brooder. I have not done this before but many people on here have said they do it and the chicks love it. I am going to try it this year. I would make sure they have chick grit available first though so that they can digest any plant material of bugs they find in the sod.