Your right about Bagdad, but I read a biography of his where he had sent some ambassadors to negotiate a trade agreement with an Islamic city in Central Asia - I think it may have been Samarkand. The Muslim ruler nailed the ambassadors to the city wall.
Bad move.
In his sixties Genghis led a huge Mongol army hundreds of miles and came up on the city from the direction least expected - the west - and levelled it.
I always liked Genghis. I might disagree with him on some points, but his methods got results.
On the positive side, he always respected ambassadors, tolerated all religions, and never used torture.
Forgive me but I thought Genghis Khan was buried in Cambodia or at least within 50 miles of the border.