I have made a lot of T-shirt quilts and I do try to avoid stitching over the design areas. What I use when I have to stitch near them or for some other reason must get close, is waxed paper; kitchen variety. It's cheap, see thru and the stitching foot glides right over it. It also tears away easily. To tear it away, I run the point of my seam ripper along the stitching line, give it a tug and off it comes.
The reason I sometimes have to sew near the design is that I like to "quilt" each T-shirt design by stitching around it and highlighting different sections of the logo before I stitch the squares together into the quilt top or add the sashing strips if using them.