Is “After his death, Confucius personally inscribed his tombstone.” true?

The Records of the Grand Historian, in the 'Hereditary House of Wu Taibo,' records in detail Ji Zha's virtuous yielding of the throne, his diplomatic missions to the feudal lords, and his hanging of his sword for the ruler of Xu, but does not mention any direct interaction with Confucius. In the novel, it is said that after Ji Zha's death, he was buried at Yanling, and Confucius, holding him in high esteem, even personally went to inscribe the ten characters 'You Wu Yanling Jizi Zhi Mu' on his tombstone. This is a completely fabricated plot by the novelist to add legendary flavor.