If he just chews it, maybe he could have cheap fleece blankets instead of towels? My Bam chewed fabric, he had his own fleece blankets, I washed them weekly and when they had too many holes in them, I threw them out. He didn’t ingest the fleece though, if a rabbits ingests a lot of fabric it can cause intestinal blockages and a rabbit that ingests (significant amounts of) non-food shouldn’t have any fabric available to him.
Bam also got lots of fresh apple twigs from pesticide free trees, he ate the bark and he was really, really good at stripping all bark of the twigs. As long as he had plenty of twigs he wasnt interested in chewing fabric.
If an adult rabbit chews a lot of non-food, his teeth could be bothering him. You can’t see the molars of a rabbit yourself due to the anatomy of a rabbit’s mouth, you need to use an otoscope to see anything and sedation is often required. Has the place that you’re fostering him for had his molars checked?