I don't know much about Black History Month, but I can't see how it can be offensive, particularly in the context of a supermarket. What are they doing to support it? If it's suggesting recipes or something, where's the harm? It can be difficult to join in things like this without accusations of tokenism, but if they are donating money to schools or community projects that celebrate Black History, that sounds good to me.
On the whole, I think that Black History should be integrated into 'history' when it comes to the curriculum, though. I read something by David Olusoga recently, and he pointed out that he learned about the Industrial Evolution at school, but it was all about mechanisation of cotton production, and not about who had picked the cotton or the families who made a fortune out of the people picking the cotton. That is pretty much exactly what my experience of history was like. I think if the curriculum expanded a bit to include the fuller picture there would be no need to separate Black History, which could be divisive and present black people as 'other'. Until that happens, though (and to be fair, maybe it has - it's a long time since either DO or I were at school) then anything that encourages inclusivity is a good thing.