Cut out the effected areas in the checkering pattern and level them. Then fill them with pieces of wood veneer glued in place. Matching as close as possible the color and grain.
All the veneer will be inside the new ch'xg pattern to be cut so any cover-up, faux-grain and coloring will be easy to accomplish.
Layout a new correct pattern to include the veneer inlays be right to the edges of the pattern so borders or edge lines will cover them easily. Cross cut inlays can be fitted at the cut of a line of checkering to hide them.
No changes in metal work are needed nor any to surrounding wood work. Just filling in what's there that you don't like,,recutting it in a proper shape that you do like,,and then blending in the new checkering to match in color, grain, streaking, ect.