Basically two reasons: experience and education.
Before understanding the differences in salaries, let me recap what undegrad and grad mean, although you may have already come across these terms. To do so, let's look at the US system.
In the US, after graduating from high school, people go to college and pursue undergraduate studies to get a bachelor's degree, typically in four years (not three as in Europe). Once they graduate from college, they're gonna work 2 to 5 years. Then, they apply to graduate schools (Medical, Law, Business etc.) and specialize into one field: MBA is one of the possible options. From that perspective, Europe's MiM programs are sort of pre-experience MBA.
Now, it is true that these MBA candidates bring in valuable experience to consulting firms. They know how to behave in the workplace, they already have a track record than consulting firms can look at, they've been trained etc. In other words, they are less risky candidates. However, experience does not fully capture the reasons behind the salary gap. After all, they can have worked in fields remotely connected to consulting like engineering (although you could arguably find transferable skills in any field).
The main reasons MBA candidates are aggressively pursued by consulting firms is that they got an MBA. Consulting firms, rightfully I think, believe MBA education is superior to other pre-experience program. A well-seasonsed public is more demanding and challenging: course content is of high-quality. Plus, not all but many MBAs are well-regarded and prestigious, and the admission process is very selective, much more so than for undergad. Hence, MBA applicants demonstrated they had what it took to get into these top schools.
Hope it was helpful,