Insert the flat edge of a putty knife into the gap and scrape it along the gap to remove as much of the loose debris as possible from inside the gap. You can also use a pocket knife or any flat object that will fit in the gap.
Suck up all of the loose debris using a vacuum cleaner. After removing the visible debris, place the hose directly over the gap and suction any remaining debris.
Place the end of a tape measure at one end of the gap and measure to the other end of the gap.
Cut a length of rope using a utility knife that is the same length as the gap. Choose a rope made of natural fibers, not polyester or other synthetics. The rope also needs to be thin enough to fit snugly inside the gap.
Fill a bucket with 2 to 3 inches of wood stain that is as close to the color of the engineered wood floor as possible. Place the rope into the stain and allow it to sit for 5 to 10 minutes. Remove the rope and lay it out on a flat on a non-stainable surface, such as an old stump, to dry.
Insert the rope into the gap and push it down with your fingers until it is as far down as possible. If needed, you can use the putty knife to help push the rope down into tight spots.