Two issues present themselves when you clean pickle juice from a carpet. The first is the stain caused by the spilled juice. The second is eliminating odor, which is caused by the vinegar and brine that turns cucumbers into pickles. Clean up the juice as soon as the spill happens to reduce the chances of both staining and lingering odor. Although you'll use white vinegar to treat the spill, it won't make the odor worse because when used for cleaning, vinegar dries without leaving any smell behind.
Firmly blot the juice with a thick, white towel to absorb the excess moisture. Only blot within the confines of the spill. Don't scrub it; the back-and-forth motion can make the spot bigger.
Combine 1 tbsp. white vinegar, 1 tbsp. liquid dish-washing detergent, and 2 cups cold water with a spoon in a small bowl.
Dip a clean, white washcloth into the cleaning solution and wring it out.
Fold the washcloth in half and fold it in half again.
Thoroughly blot the spill with the washcloth until the area is saturated with the cleaning solution.
Fold another clean, white washcloth in half and in half again.
Blot the washcloth against the spill area until all of the liquid is absorbed.
Repeat Step 3 through Step 7 as needed until the juice is removed.
Let the spill area completely dry. If the site is located near a source of heat, like a window on a sunny day or a heating vent, lay a towel over the area as it dries. Heat will cause the odor from the pickles to set in the carpet as the moisture dries.
Place a large box of baking soda near the spill to absorb any lingering odor. The box might need to sit for a few days or weeks to pick up the scent. If this solution isn't feasible due to the spill being in a heavily trafficked area, apply a household odor eliminator according to the directions on the package.