i have an 18 month old golden retriever and she eats everything...shoes, barbie dolls, dvd's, the carpet, and all kinds of clothes. very rarely does she have a problem. every now and again it will upset her stomach a bit but that is it. it is really much more annoying for me than anything but if it's any consolation, they do usually grow out of it! good luck
One of our pit bulls ate my mother's paperback book that she was reading, when I was a teenager. No problem for him. We never even thought about taking him to the vet. My mother was just mad.
If she has not appeared to be ill by now, I would not worry about it. A 7 month-old pit bull should be big enough to eat and digest an 8" square piece of cloth, if I understand correctly what she ate. You should start seeing some of it come out the other end any time now, if you have not already. It might come out all at once, or it might take it a few days, a few little shreds at a time. I hope that she did rip it up and chew it into pieces. If she ate it whole, I would be more worried about it causing a blockage than if she played with it and ripped it up.
But since you posted 20 hours ago, if she does not show any symptoms of illness by this time, I think you are in the clear. If it happens again, I would just watch her closely for about 24 hours or until it starts coming out. The only dog that I personally know who got a blockage from eating a foreign object was a Rottweiler who ate an entire adult tennis shoe, mostly in one piece. There was another dog at my vet's office, a Boston terrier, who ate rocks, and I saw the x-ray -- you could see the rocks in his stomach. Those are the kinds of things you really need to worry about, more than you need to worry about a pit bull ripping up a handkerchief. We had pit bulls in my family when I was growing up, and from what I remember, that was pretty much what life with pit bulls was like