Remove furniture from the space before attempting to clean or remove the scuff marks. Sweep the concrete floor with a dust mop or broom to remove any loose dirt, dust or debris.
Slip on a pair of rubber gloves, respirator and safety goggles before creating a mixture of 1 tablespoon of trisodium phosphate and 1/2 gallon of lukewarm water. Stir the water until the trisodium phosphate powder is dissolved.
Dampen a plastic scrub brush with the mixture and work it into the scuff marks. Continue to work the TSP solution into the scuff marks until they are completely eliminated.
Wet a kitchen sponge with warm water and use it to rinse away the TSP. Do not allow any TSP solution to remain as it can cause discoloration or streaks.
Dry the floor with a towel or allow it to air dry completely before replacing the furniture.