oh no...not paper!
I know it seems "green" and frugal to repurpose newspaper, but I just chuck it in the recycle bin. With that said, I DO love this method of using up scraps. What I do is wait until I can get a 50% off price at Joann's and then I buy a whole bolt of thin cheap muslin. I cut 6.5 inch squares and use them instead of the newspaper. I use up my scraps and then have a huge pile of these sturdy and lovely squares. I have made tons of "give-away" quilts by just using sashing to finish the quilt top, added batting and backing, and then quilt in the ditch to finish.