Biting at the cage bars.

[ShinyRainbowWaffle]

I have had my two newcomers, Tinkerbell and Periwinkle, for a little over a week now. They had gotten along just fine with me for the most part as I made my rounds and refilled their food, hay, and vacuumed up their droppings. Tink didn't really care when I was cleaning and Peri would follow me and "chase" the vacuum. (It's a small, handheld one.)
After I had changed their fleece for the first time, Periwinkle began to bite at the cage bars on the bottom level and dig and bite at the fleece liner I just put down. Whenever my fingers would get too close to her mouth, she nipped them and would sometimes try to pull them into the cage with her. (She did this to my friend who was visiting as well.) No blood was drawn, but they were sharp bites in comparison to Peri's usual nibbles. I'm assuming it's her getting territorial on top of still having to adjust to the new environment, but any insight is appreciated.
She has continued to do this digging and biting behavior, and the triggers seem to be if I am in the room for "too long" or if I am opening the bottom doors to the cage. My main concern is if she keeps up this biting behavior, what is the best way to go about making her stop?

 

[Godofgods]

ive had that type of thing happen with some of my chins. For some reason something just triggers in them and they get all worked up and start going crazy. Biting bars, chewing or ripping up anything they can get there teeth on. I think its just a bunch of pent up energy or like an adrenaline serge type of thing. Ive never rly been able to calm them down.

 

[Sadiechinchillalover]

My Blossom does the exact same thing when she wants to get out and play. She's not meaning to bite your fingers; they just get in the way when she's trying to escape! Haha I wouldn't worry about it. All of my chinchillas do it here and there. Blossom does it the most though!

 

[ChinChild]

Our younger chin Mojo is a little maniac, and he does this all the time too. Don't get me wrong, he's affectionate as can be & isn't the least bit aggressive, but he's very mouthy. He chews on ANYTHING, and he hardly ever sits still. No matter the time of day, if you walk up to the cage & open the door, he will want out. So I know he's got a ton of pent up energy, and on the nights where I don't have time to let him out for very long, he'll start doing exactly what you were describing: chewing the cage bars, pulling up the liner, throwing his furniture around, and scrabbling at you for attention. He's a happy lil bugger, so I wouldn't think it's anything to worry about - at least in my experience.