Set the partial vinyl tile or tile scrap over the burnt area and align it with the pattern on the burnt tile. Line up a steel ruler where you want to make the cut. Run the utility knife against the edge of the ruler and cut through both layers of tile. Keep realigning the ruler and make the next cuts until all cuts are complete.
Set the patch aside and pry up the damaged area on the tile, using the utility knife. Scrape away any tile mastic left on the floor, using the putty knife. The floor surface must be smooth so the new patch forms a strong bond with the floor.
Spread tile mastic with a notched trowel over the bare floor where the burnt spot was. Align the patch with the tile design and press it into the floor. Cover the patch with wax paper. Place three heavy books over the patch to press it flat to the floor. Allow 24 hours for the patched area to dry.
Mix the two-part seam sealer in equal amounts in the included applicator bottle. Apply the sealer along the edges of the patched area by squeezing the applicator bottle.