I would lay it out flat, wrong side up, and mark seams where excess fabric is causing "pillowing". Take to sewing machine and just sew over existing seams except making the seam a little bigger in the areas of excess fabric. No need to rip out any seams as none of this extra stitching will show later. I would do this before starching and ironing, or blocking, to minimize the amount of excess fabric.
The likely cause is that the white strips were cut a bit off-grain, resulting in slightly bias edges that stretched when you sewed the strips. Spray starching the strips before sewing would have stabilized them and prevented this; however, spray starching precuts can create a different problem if the strips shrink. With this kind of pattern shrinkage would not have mattered, so it would have been preferable to starch before sewing.
Some of the excess will "quilt out", but it's best to minimize the excess as much as possible.
Last edited by Prism99; 07-27-2017 at 06:23 PM.