This question is a translation of russian “какая разница?” (which literally means “what is the difference?” or “is there a difference at all?”) but it has two appalling meanings in russian.
The legend says that after russian empire occupied Western Ukraine (probably in XVIII century), some Ukrainian representatives came to the official governing the region and asked for giving Ukrainian language a higher status, for example make official announcements in Ukrainian. The governor asked them if they understand russian language and after they said yes he asked what does it matter then which language to speak. Since those times the question is used as a marker of russian chauvinism (and of course a narrative that russians push): why should local languages and culture matter if the colonised nations understand russian?
The other meaning is for the everyday use. In this case it means “this thing is trivial and not worth discussing, so let’s forget about it”. Of course it’s often used to evade the blame or at least an inconvenient question as in “—Who broke the window? —What does it matter, we should think about replacing it.”
So why I’m writing about it? A third meaning to the phrase seems to appear and it does not serve their agenda this time. I follow the news related to the war and a good deal of them are about russian officials making inane claims, saying outright lies and spitting completely unscientific bullshit. And usually their newer statements contradict previous ones so you either need to have the memory of a goldfish or be well-trained in doublethink to believe them. So what does it matter what they say? After all this time the only thing that should be taken into account is their actions and what they said should interest only the judges at the future tribunal.