I was given advice by 3 80 year old ladies to use a sheet on the back of my first quilt. I hand quilted it just fine. Or so I thought...until I hand quilted my second one and discovered how much easier it was to needle when I had LQS fabric on the back!!
You have it; use it to machine quilt.
And if the sheets still smell, hang up a temp clothes line outside. It will be worth it.