It has been a long time since I read Consider Phlebas, which was my first introduction to the Culture and started me on the road of reading most of Iain M. Banks works in that setting.
I remember that Bora Horza Gobuchul was a Changeling working on the side of the Idirans during the Culture/Idiran war that is the background to the novel, and he was selected by the Idirans to attempt to retrieve the Mind after it ended up inside Schar's World, because he had spent time there previously.
I remember that the end of the book included a number of facts and figures about the causes and effects of the war itself, and IIRC there was a few sections in the novel which showed that the Idirans didn't utilise Artificial Intelligence in anything like the same way or degree that the Culture did. If I remember correctly the Idirans used computers but ensured that those computers were fully under control of an organic Idiran.
With this in mind I was wondering what reason the Idirans wanted the Mind for? Was this addressed at all in the story (and I've forgotten it?) or was it not stated and Iain M. Banks later explained this plot point?