As-salam aleikum wa rahmatullahi wa baraketuh, brother
the passage related to the woman taken in adultery does not belonged to the original Gospel, in fact it is a later interpolation inserted into the text, and it is rejected nearly by all Christian scholars today. It is not found in the earliest and most important manuscripts. Prof. Bruce Metzger states also that no church father referenced the story prior to the twelfth century.
See Bruce M. Metzger, A Textual Commentary on the Greek New Testament: A Companion Volume to the United Bible Societies' Greek New Testament, 4th Revised Edition, (Stuttgart: German Bible Society, 1994), p. 188.
Jesus (pbuh) would not contradict the Torah, he came to confirm it. The Christians however, seems does not liked the idea of stoning as a punishment for adultery, so they invented this illusory story in order to show that Jesus do not condemns adultery which is of course a lie. According to a certain conversation between Jews and Prophet Mohammed (pbuh), it can be conclude that Jews also hated the stoning despite the fact that it is a part of their Law.
Take care, and salam
Ahmed (Poland, Warsaw)