So what is the mass of a byte of ‘pure’ information? And how do you derive it?

That's all in the linked wikipedia article, but since you asked:

At room temperature, the Landauer limit represents an energy of approximately 0.018 eV (2.9×10^−21^ J).

That's 1 bit, so 1 byte is eight times that, which you can plug into E=mc^2^ to get its absurdly small equivalent mass.

It's important(?) to note that Landauer's Principle is not settled science and has yet to be rigorously proven, unless there's some recent development which the comic is referencing. I haven't checked.

Go back to school