Tikka Masala is an Indian-Inspired dish which was invented in the UK by people with Indian cultural heritage. That's about as concise a description as you can get without running into difficulties of definition - there's no consistent way of defining what "being a dish" means without running into contradictions.

In fact General Tso's is the perfect counter-example: Multiple Chinese people have told me they enthusiastically disown General Tso's Chicken and explicitly call it American food. So if we say "a dish belongs to a country if it's invented there", then Tikka Masala is British (which I agree "feels" wrong); but if we say "a dish belongs to a country if it was inspired by the cuisine of that country", then General Tso's is Chinese, which, apparently not!

And that's without even considering the question of how far "back" you should go with inspiration - what if a dish was inspired by how the Indians used food they got from the Persians who traded it with the Chinese - is it Indian food or Chinese food? (Idk if that's historically nonsense, but you get my point) Why is the most-recent ancestor more important than the environment of creation?

I respectfully disagree with one major caveat. I'll get that out of the way first; I think there should be a name for these foods that recognize the creators (e.g. Italian American food is American food that comes from Italian immigrants). We've traditionally been bad at giving credit or, worse, using names to mark a cuisine as "other" and weird.

The thing is that there really isn't a food of a place. People use ingredients that are available and use techniques from the people around them. When cultures interact, they create remixes of cuisine that take unfamiliar ingredients and techniques and create something new.

Let me use the food of my own home, New Mexico, as an example. The food of the region is a mixture of Spanish colonizers, later Mexican immigrants, and Native American foods using a crazy combination of techniques and ingredients from all three. It isn't Spanish food. It isn't Mexican food. It isn't Native American food. It is New Mexican food, a thing that arose from a place and its history. Now, with Asian immigrants moving in, the food has started to incorporate stuff from those cultures too.

Is deep dish pizza considered American, Italian, or culinary cancer?