Look, if you want to argue about this because you're bored, we can do that. But I think that if you ask the average English speaker, "Is babushka an English word?" most of them would say no.

The way it is used in English (as "headscarf") is completely limited to talking about the headscarves of Russian peasant women - no one would say, "Oh, it's windy outside, let me run back in for my babushka." Or, "Oh, did you see the babushkas they're selling at Macy's? They are sooooo cute."

It's in the dictionary because if you're reading a book and come across the word printed in English (as will happen if you like to read Russian literature in translation), with no explanation or hints from context of what it is, you need to be able to look it up. But the fact that it's in the dictionary does not mean it's "valid" English. That would be like say "glasnost" and "perestroika" are valid English words because you can find them on dictionary.com...but the truth is, we use them only when referring to Gorbachev's reform policies. In English, you wouldn't say about your American company, "Yeah, we're having a perestroike - they're firing all the middle management," because we already have the word "restructuring."