freezer paper DOES NOT LEAVE ANY RESIDUE ON YOUR FABRICS, NEEDLES OR ANYWHERE ELSE. The plastic coating will 'stick' to fabric (or other surface it is adhered to) but peels off without leaving any residue behind.
and usually when using it for piecing you do not actually stitch through the paper, you stitch beside it. your freezer paper is actual size, the seam allowance is added to the fabric so you can stitch beside the paper.