Vacuum the walls with a wet/dry vacuum to remove as much soot as possible.
Fill a bucket with 1 gallon of hot water and add 1/4 cup of trisodium phosphate. Stir the solution with a spoon until the trisodium phosphate fully dissolves. Put on rubber gloves.
Dip a cloth into the bucket and wring it out. Wipe the soot stains with the cloth, limiting scrubbing to the stained area to avoid spreading the soot. Rinse the cloth in the bucket and wring it out as needed.
Rinse the walls with a clean, damp cloth. Allow them to air dry or dry them with a towel.