Hmm. I can't help but feel like Mathilde presenting herself as a representative of the Empire looking to fulfil ancient oaths is a bad idea, mostly for two reasons.
Firstly... claiming that is a massive overreach. She's not here on the orders or request of another, and the Empire itself is providing no formal assistance to Belegar's mission, which is why he got frustrated and decided to put out the call for basically anyone who wanted in to come meet him. Framing the appearance of a single wizard as a sign of oaths repaid kind of cheapens their value and highlights how the Empire is only sending a single wizard, rather than a small army of professional troops.
Secondly... well, it's not true. Mathilde isn't going to Karak Eight Peaks because of her ancestor's oaths, she's going because she wants adventure, or perhaps just to get well clear of the Empire for a bit and find herself. The professional relationship she has with Belegar is going to be incredibly important for her chances of survival and glory, so I strongly recommend against lying to the dude on the first meeting.