Have you tried pressing it? I know it sounds weird, but some tear-aways change texture when ironed. I used to use tons of tear-away, and preferred the heavier, because I could almost snap it away from the stitches. I wouldn't worry if every bit does not come out, because once it gets washed, you won't be able to tell.
When I get ready to tear it away, sometimes I take the backside of the seam ripper point, and run along the stitch lines. That seems to perforate the interfacing enough to make the job easier. For a blanket stitch, I would run it next to the straight stitch end, then come back and do it at the same level as the legs. tear the big pieces off, and give it a good shake outside. Try it on a small area. and you will see what I am trying to explain.