Put on rubber gloves and place a piece of fine-grade steel wool on one of the engineered floor scratches.
Look at the surrounding area of the board and determine which direction the wood grain runs. The wood grain looks like very thin lines that all run in the same direction.
Rub the scratch using firm pressure and following the same direction as the wood grain. Concentrate more on the outside edges of the scratch to smooth them and blend them into the surrounding floor board.
Open a pack of wax-based wood repair sticks. Locate the wax stick that mostly closely resembles the color of the engineered floor. Rub the end of the wax stick over the scratch to fill it in and to color it.
Rub the piece of steel wool very lightly over the repaired area, simply to sand the wax down to the same level as the top of the wood. Run your bare hand over the area to determine when it is even and smooth.