Personally I'd be more interested in an ETS bandanna, that was printed with suitable survival info and the ETS logo.
I'm aware of some existing products. Eg there's a common one sold by TAD Gear and other places, and there are two mentioned at the bottom of AMSEA's website. However, ETS could have its own. Wouldn't silk be a better material than cotton?
The bandanna could be a large one : silk would make it easier to store in a pocket. But you could not use it (if silk) to grab a hot cooking pot handle for instance...