The Mongols under Genghis Khan did invade parts of India during the reign of Iltutmish.

During the 13th century, the Mongols, led by Genghis Khan`s grandson, Hulagu Khan, launched invasions into various regions, including Central Asia and parts of the Indian subcontinent. In 1241, Mongol forces under the leadership of a general named Chormaqan crossed the Indus River and invaded Punjab, which was ruled by Sultan Iltutmish of the Delhi Sultanate.

The Mongol invasion was fierce and resulted in the sack of several cities, including Lahore. However, due to internal conflicts within the Mongol Empire and the death of the Great Khan Ögedei, the Mongol forces eventually withdrew from the Indian subcontinent. The invasion did not lead to a prolonged Mongol presence or direct Mongol rule over the region, but it had an impact on the political situation in North India during that period.

Once again, I apologize for any confusion caused by my previous response, and thank you for bringing it to my attention.