Love this quilt, it is just too cute. So original!
I like the grass on the bottom idea. I would use the same background as you used in the squares and applique the same style of grass. This way you use the same colors you already have in the quilt, you can make the size as large as the squares if you wanted to, although I would make them smaller so as not to detract from the tiger squares.
Whatever you choose to do I am sure it will be beautiful.