Yes, muslin was used on the backs of most quilts in years gone by. Remember the quilt tops were usually made from scraps, old clothes, limited new purchases...a practical way use everything....waste not, want not. It's only recently that prints were promoted to be put on the backs....great move by the textile mfgrs.
i put muslin on the backs of quilts, wallhangings.....a good quality muslin, when washed, is soft as butter.....(for bed quilts). On wallhangings I use a cheaper grade..why not?
.....and I read somewhere that calicoes are coming back in the spring...maybe a bit more updated, but nonetheless calico.
those bow ties look a lot like a mosaic design when put together as they are. And that center square is usually the same color as the edge squares....your mom had a great design eye when she planned these blocks...