‘Ā’ishah (may Allah be pleased with her) reported: Some people said: "O Messenger of Allah, meat was brought to us by some people, and we are not sure whether the name of Allah has been mentioned on it or not (at the time of slaughtering the animals)." The Messenger of Allah (may Allah's peace and blessings be upon him) said: "Mention the name of Allah upon it and eat it."
In this Hadīth, ‘Ā’ishah (may Allah be pleased with her) says that some people came to the Prophet (may Allah's peace and blessings be upon him) and asked him about meat that they had received from Muslims who were new converts and were not yet familiar with the rulings of Islam. It was not known whether or not they had mentioned the name of Allah when they slaughtered the animals. The Prophet (may Allah's peace and blessings be upon him) told those people to mention the name of Allah before eating the meat. He said in another narration: "You mention the name of Allah and eat." It is thus evident that he wanted to say to them, in a reproaching tone: you should not care for what others do if the thing is apparently lawful. Rather, you should care for what you yourselves do, so mention the name of Allah and then eat. Accordingly, if a Jew or a Christian offers meat of an animal that he has slaughtered to a Muslim, the Muslim should not ask if the animal was slaughtered in the Islamic manner. This question is irrelevant, for it goes too far. This does not mean that the slaughtered animals regarding which one is sure that the name of Allah was not mentioned over them are lawful.