Place a few paper towel sheets loosely over the spilled Betadine, and allow them to soak up any excess Betadine that hasn't seeped down into the carpet fibers yet. Toss the soiled paper towel sheets in the trash.
Pour rubbing alcohol over the Betadine stain, and let it sit for 60 seconds. Blot up the liquid with a clean white rag. Always work from the outside of the Betadine stain inward.
Apply a dry-cleaning solvent to any Betadine solution that still remains in the carpet. Blot again, but with a fresh white rag.
Mix 1 teaspoon of sodium thiosulfate and 1/2 cup of warm water in a spray bottle. Saturate the stubborn Betadine traces that still exist in the carpet with this solution. Wait five minutes before blotting the area clean.
Flush the carpet with cold water once the stain has been removed. This will help to get rid of any cleaning product that may still be in the carpet fibers. Blot dry with a clean white rag.