I've watched every season of the new Top Gear and about half of the old ones and always dreamt of the day when Top Gear would come to my city in India. They did, but I wasn't there, and their coverage was overwhelmingly negative. Highly disappointing. The first shot of my city is a video of someone pissing on the street. That's like introducing NYC by showing a crackhead smoking openly on the subway.
Jeremy being himself was highly inconsiderate with people's lunchboxes in Mumbai, but that wasn't offensive as such and those boxes were probably just props. The thing they did with the train was slightly offensive but really not that bad. The most offensive thing was James putting a Ganesha idol on the hood of his Rolls Royce instead of on the dashboard where it's supposed to go. It's really subtle but makes a huge difference because out here people consider idols to be an embodiment of the actual deity, and you would never tie somebody to the front of your car and race it unless you were trying to torture them. Poor James: he was really trying to be as PC and respectful of the culture as possible but it failed.
As a huge fan of the trio, I don't think they're all that offensive when they intentionally make a joke about this or that culture or demographic. Their jokes (even the offensive ones) have good entertainment value and tell it like it is. They only cross the line when they do something racist or offensive inadvertently (like that car in Argentina, or the slope joke, or the n-word slip, or the Ganesha idol), and those are the instances that they need to avoid by, say, including an actual local in their production crew.
Also, Grand Tour is a shitty name for the show. I hope they go with something else.