As an Asian-American, I did find that tweet offensive. And not only was it offensive, but it wasn't even a clever joke, either. Making fun of Asian accents is so tired. Come on. Put some effort into it, dang!
It wouldn't surprise me if Japanese people in Japan do not find it as offensive, because, as the dominant group in their country, they do not have as much experience being victims of racism and are therefore probably not as sensitive to it as Asian diaspora (e.g. myself) would be.
Asian-Americans (or Asian immigrants in the US) and Asians living in Asia are different. You are right about that.
Mao is not an Asian-American and obviously a foreigner from Gracie's standpoint. English is just a foreign language for Mao that she does not need to speak daily. I don't think Gracie would have said something like this if Mao was someone living in the US.
To me, if people living in totally different parts of the globe make jokes about one another's differences in a light-hearted way, it is perfectly fine. But if someone make fun of another living in the same community or country because of his/her accent, it's a totally different issue.