I have only backed one quilt with Minkee but I too could not bring myself to throw away the scraps which were a decent size. I ended up with strips about 6 to 8" by WOF and also some narrower strips. The quilt was a gift so I used some of the narrow strips to make a "ribbon" for the quilt. I folded it up and tied the ribbon of minkee around it. Then I took one of the wider ones and fringed the edges and included it so the little girl who got the quilt could use it as a winter muffler/scarf. I still have one decent size scrap left that is about 6" or so wide by about 24" long. I put it in my scrap stash.
I have seen people use small squares of minkee in fidget quilts. I was thinking they might be a fun addition to a child's quilt because they don't fray so you could do a raw edge applique with them and sew those down to a kids quilt to have little pops of soft for them to "pet".