Choose tulle. I chose a lavender tulle. Go darker, if desired, instead of lighter. If you use white or very light, all you see is the tulle. If chosen right, you will not notice the tulle covering. Cut tulle a little larger than the piece.
After trimming the tulle and yarn to the edge of the muslin, machine stitch 1/8" from the edge.
This is what it looks like after basting and machine stitching. (Hope your stitching is straighter than mine).
You can adjust the design elements by inserting a needle horizontally under the tulle and pushing to compact the yarn into a finer line. Embroidery will take care of the rest.
Here is the finished background compared to the original picture.