According to Wikipedia [1] the dish chicken tikka masala is thought to have been invented by Bangladeshi chefs working in the UK in the 1960s. Doesn't that make it at least somewhat British? It was invented by chefs in a different country than their own, likely then adjusted by those chefs to what they perceived that the local market wanted. In contrast, I mean, to being cooked "The Way It Has Always Been Done" in their country's tradition?
The Wiki page even mentions more classical/historical dishes from the norhern Indian area, that are thought to have inspired tikka masala. That, to me, makes it even more clear that the dish is new.
If I, as a Swedish person, move to the US and compose an awesome recipe for pizzaballs [2] where I combine Swedish meatballs with the American love for all things pizza [3] and it becomes a huge hit which is exported to the rest of the world, would that make the dish Swedish?
[1]: https://en.wikipedia.org/wiki/Chicken_tikka_masala
[2]: I'm just making up an example here on the spot.
[3]: A love which is, of course, shared by large parts of the rest of the world in our own fashion, not trying to point the finger at (a nuclear superpower of 330 M people) y'all in any way.