Sprinkle baking soda across your jute carpet. Let sit for 15 minutes before running your vacuum over the rug to remove the baking soda. Repeat this process once more. This process should help absorb most of the odor.
Take your jute rug outside and let it bake for one day in the warmth of the sun. The dry heat will help remove any humidity that is contributing to odors that originate from the jute itself.
Lightly spray some air freshener (Febreze is safe on Jute) near and around the carpet. Let the rug sit in a room with good ventilation. If your room has poor ventilation consider placing a fan near the rug.