Mary, the quilt is beautiful and your thoughtfulness in sharing the leftover square for a gift for your friend is awesome.
Before I learned to quilt I commissioned a wonderful quilter to make a quilt for the birth of each of my three grandchildren (over a 7 year period). When I picked up the youngest child's quilt she presented me with a small quilt made with small scraps of material she had from all three quilts. I treasure that quilt and will never forget her thoughtfulness. I'm sure your friend will treasure your gift.
Quilters are the best people.