Popper does not have a monopoly on the definition of 'science.' For example, quantum mechanics is not exactly falsifiable... And the general idea of falsifiability has been criticized by many, including non-Marxists.
When Marxists talk about it being 'scientific socialism,' they are contrasting with 'utopian socialism.' Scientific socialism takes the approach of examining the world, making changes, seeing how those work out, and then re-examining the theory. You can see how that relates to the scientific method.
Quantum mechanics certainly is falsifiable. If the electron two-slit experiment produces a pair of humps, it is falsified to extremely high confidence. (Also, we'd have a hard time dealing with the Pauli exclusion principle, and therefore solid matter, without quantum mechanics.)
Marxism is not scientific, as it does not attempt to falsify one of its core axioms—that the class struggle is over a local optimization game. A central committee can actually do a pretty good job of adjusting the ratio of copper tubing to copper wiring, but the actual challenge turns out to be making people want to invent things like graphene.
My physics knowledge is pretty limited, but I was under the impression that it's at least controversial.
Regardless, you're not engaging with my core point, which is that 'scientific' in this context means something specific, not whatever you happen to think scientific means. Nobody is claiming Marxism is falsifiable, that's a red herring.
When Marxists talk about it being 'scientific socialism,' they are contrasting with 'utopian socialism.' Scientific socialism takes the approach of examining the world, making changes, seeing how those work out, and then re-examining the theory. You can see how that relates to the scientific method.