I would spray both sides of each towel that was washed with their stuff with Fabreeze.

There are molds that will stick tenaciously to surfaces despite those surfaces having been cleaned. When tenants move out of apartments I often find that there are stains in the stainless steel kitchen sinks that don't come off with regular washing. The stains have to be killed with bleach, and that means they're alive. I expect what you have is mold that's sticking to the towels tenaciously and needs to be killed somehow. As bleach would discolour the towels, I'd try using Fabreeze.

Bacteria and fungii are very sensitive to the pH of their environment. If the Fabreeze doesn't kill the smell, I'd try rinsing the towels in a 10:1 solution of vinegar in water (1 part vinegar to 10 parts water). That should kill the bacteria causing the smell.