To what extent is the authenticity of the hadith "Erase it, O Ali," mentioned in the story of the Treaty of Hudaybiyyah?

The Hadith (definition) is authentic. Ali's refusal, may Allah be pleased with him, to erase the words "Messenger of Allah" from the document was not an act of disobedience, but rather an act of reverence and glorification of the Prophet, peace and blessings be upon him. This is similar to Abu Bakr's refusal to lead the people in prayer when the Prophet, peace and blessings be upon him, was present, and like a dutiful son who refrains from sitting at the head of a gathering out of respect for his father. Thus, Ali understood that the command was not obligatory.