بسم الله الرحمن الرحيم
Careless story tellers and Khuttab mention the story below to prove the kindness and mercy the Prophet Muhammad ﷺ came with, however we have many authentic stories to relate instead of lying upon the Messenger of Allah ﷺ and making a place for ourselves in the Hell Fire. May Allah protect and save us from the Hell Fire.
It goes that a Jewish woman in Mecca who would throw garbage on the doorstep of the Prophet (peace and blessings be upon him) in defiance of his message, and one day she fell sick and could not throw the garbage, so the Prophet (peace be upon him) visited her. Then it is said that she was so amazed at his character that she realized his prophethood and accepted Islam.
I tried asking the people (the Jumuah Khutaba) who narrated this fabrication and lie as to where they got it from, but to no avail.
Never could anybody present this story from any reliable source, i.e. Hadith books, one of those who claimed proofs for this presented nothing but a reference to a small story book on The Seerah of The Prophet ﷺ, which is again not an authority on the topic.
Saheehus-Seerah 