Something else to consider is that staying here allows us to get to know another member of Belegar's council, one that we're likely to be working with closely through the rest of the campaign.
We have to remember that as much as we like the dwarves, our goals are not their goals. The dwarves need help taking K8P and we're helping with that, because we like them, but also because it'll get us Dwarven Rep we can use to get dwarven goodies. Their victories are only tangentially our victories. If we have an opportunity to help out in a way that benefits us, the only reason not to take it is if the difference in Rep we expect to earn elsewhere outweighs it.
Well, yes and no. Being seen by the dwarves not to have a selfish agenda and simply to have come to fulfil the terms of the ancient pact between the Men of the Empire and the Dwarves or Karag Ankor is likely to accrue favours at a faster pace than being seen as being more obviously grasping.
More strategically, having an agent of the Empire's central government being a key part of successfully retaking of Karak Eight Peaks is diplomatically very useful, both internally and externally. Externally, as far as dwarven relations go, Mathilde's contributions should easily cover for the fact that the Emperor only 'sent' wizards. Internally, it should strengthen the position/legitimacy of the Emperor vis-a-vis the Elector Counts, as he sent aid to the dwarves and they didn't. The Empire is still lately feudal, and this kind of obligation is the lifeblood of relations between and within the various strays of society. If people see you not fulfil their obligation to help someone else, it will make them doubt whether you'll fulfil their obligation to you, so they'll look for other allies or sponsors. Plus, the religious aspect I mention later will have implications for the Emperor and Elector Counts.
This may well earn her College Favours, as the Emperor will owe the Colleges for saving face for him, and the Colleges will owe Mathilde. Not to mention the amazing advertisement that she's been for the potential of Imperial Wizards to the dwarves. Within a few years sufficiently sensible Imperial Magisters may well find dealing with dwarves a lot easier, which will be worth a lot, particularly to the Gold College.
There's also a religious aspect here, as helping the dwarves is an obligation according to the Cult of Sigmar. We may earn favour with them as a result, which may similarly be parlayed into College favour.
Even if it could be done I'd say we do not wnt that amount of imperial attention. Between the Book That Must Not Be Named and just being a magister of the grey College, the very shiny title of Hero of the Empire does not suit us.
On the other hand, there are many ways to be a Grey Magister. The brightest light casts the deepest shadows, after all.
I think the book is a non-factor to be honest, particularly if we set up shop at Karak Eight Peaks for the medium term.
If Mathilde is an instrumental part of the initial retaking of the peaks, I could easily see the Empire reinforcing success, jumping on the bandwagon by sending more troops. That's the point where for she might be declared a Hero of the Empire for political purposes, to make it clear that she's been operating in an official capacity.