Thanks everyone for the great ideas. I had tried Fabreeze before I posted the question and it wasn't taking the smell out. I don't know why I didn't think of the vinegar because I use white vinegar so much for cleaning and washing. It hadn't occurred to me to just soak the fabric so it didn't fray. A friend had suggested dryer sheets but I didn't have any on hand. The odor eater shoe inserts is a great idea. I've put that in my resources for future use. I hung the strips outside for a couple of days and that did the trick.
I'm so glad I was able to save the fabric. Even though I don't know the person who cut and sewed the pieces she is a fellow quilter and I wanted to honor her efforts by completing something she started. I so appreciate all the suggestions posted here and hope others have gained something from it too. This board and the people who are on here are the greatest!