He visited Muawiya, who asked him about a hadith and instructed someone to write it down. Zayd said to him, "The Messenger of Allah ﷺ commanded us not to write down anything of his hadith." So he erased it.
حدثنا نصر بن علي أخبرنا أبو أحمد حدثنا كثير بن زيد عن المطلب بن عبد الله بن حنطب قال دخل
على معاوية فسأله عن حديث فأمر إنسانا يكتبه فقال له زيد إن رسول الله ﷺ أمرنا أن لا نكتب شيئا من حديثه فمحاه
Sourcing, its isnad is daif. Ahmad reported it in 5/182 from Abu Ahmad Zubayri, through this route.Muttalib bin Abdullah did not hear from Zayd bin Thabit, as stated in Jami Tahsil, p. 281, nor is his meeting with Muawiya established.