Maybe show a small reputation bar under contract type name? Yes, this will double the number of lines, but it will be more visual and will not interfere much, because these are pop-up signs. It seems to me that it would be quite convenient for additional orientation in information.)
If this is not a good option, then you can display reputation numbers next to the icons of the houses involved in the contract (but it seems to me that the reputation bar is much clearer).

Like this[dropbox.com].
I apologize for curvature. I just made an example from segments of several images.

Oh! And I forgot about the information about negotiation points! I forgot to include them in the example image. Their icon can be placed a little to the right of the Reputation bar. I can make a new example if you need.
[and sorry my bad english... >_<"]