A very crazy way indeed!
The burning sensation combined with the hot water from the bath will cause the skin to sweat more. This will cause the natural body fat to partly come off the skin.
The ice blanket will cool the skin. This contracts the sweat glands and the fat-producing glands in the skin, causing them to expel even more fat.
The grossness you see on the blanket is simply skin fat, possibly combined with some remains of the garlic, the ginger and the pepper.
This has nothing to do with detoxing.