This is a really good question - of course the samurai will have left a mark on Japan – but not one I can directly answer: 20th century Japan is not my thing. However, I can tell you it’s going to involve unlearning what you’ve already read about the samurai themselves. Nitobe and his concept of “Bushido” are the biggest pitfalls in Japanese history. To quote Cameron Hurst in his essay, Death, Honor, and Loyalty: The Bushido Ideal.

One wonders whether the modern Japanese themselves, let alone those of us in the West, would ever have heard of bushido had it not been for the efforts of Nitobe Inazo (1863-1933). In almost every way imaginable, Nitobe was the least qualified Japanese of his age to have been informing anyone of Japan's history and culture.

There are some good posts already on Ask Historians about Bushido, so I won’t reproduce them. Check out

Was the way of Bushido ever documented in a book, if so what should I read? answered by /u/bigbluepanda and /u/ParallelPain . They recommend some good journal articles and books on the subject, but I’m going to link to some open-access versions of articles on Bushido, in case you can’t access JSTOR or a quality library.

• Bushidó or Bull? A Medieval Historian’s Perspective on the Imperial Army and the Japanese Warrior Tradition By Karl F. Friday. This addresses the question of whether there’s a continuity over all those years from medieval samurai to WWII, so it should be interesting to you.
• Death, Honor, and Loyalty: The Bushido Ideal By G. Cameron Hurst III. Gives the full story of how Nitobe and others misread and cherrypicked sources to create a new modern ideology of Bushido.
• The Historical Foundations of Bushido by Karl Friday. I like this one because it’s actually an archived version of a post Karl Friday made on a martial arts board answering members’ questions. A historian who is out there dealing with the public and writing in plain, readable language: my hero!
• /u/ParallelPain mentions Oleg Benesch’s book, Nationalism, Internationalism, and Bushido: Inventing the Way of the Samurai, as the book on the modern development of Bushido, but if you want to check Benesch out but can’t access his book, his entire PHD thesis is open-access: Bushido : the creation of a martial ethic in late Meiji Japan

Bushido's an invented tradition, but one with real influence on 20th century society. In pre-Meiji Japan, most people weren't samurai, and didn't idealize samurai honour or aspire to follow such a code themselves. Modern Japan often does idealize samurai honour and continuously redefines "Bushido" as an aspirational code for everyone. In Imperial Japan, samurai honour was redefined as unquestioning loyalty to the Emperor. Today "Bushido" in Japanese pop culture is often about being true to your values, even when it means going against authority. It's an interesting transformation.

It doesn’t fit in with the rest of the discussion about Bushido but directly regarding your question, /u/white_light_king posted some hard numbers on percentages of samurai background in the Imperial Army in the late 19th century into the 20th century.