Betty Jo, I think I would sew (slip stitch crochet) the block to the strip. I think that is what your mother was doing. I would then go with the cream background, appliquing the crochet strip to the pillow area of the quilt. Of course I would not let anyone use the quilt :shock: to protect Mom's work. Just my thought on it. The crocheting is beautiful, and for it to be your mothers is priceless.
A second thought: It could be backed with a dark color and used as a table runner for your dining room. Back in the day
, crocheted bedspreads and tablecloths were popular. I would guess she was planning on it to be one or the other.