That number also represents the effort that the aliens have put in to your opinion of them, in an effort to make peace with you. However, I do agree that your diplomats should be able to find out something of their opinion of you. Even if they could only find out if it was positive/neutral/negative it would be an improvement.
But generally if you are using a small commercial–engined diplomatic ship, and it’s the only ship in their territory, then their relationship with you will be going up even if they are asking that ship to leave every week. You get a penalty from having your diplo ship in their system, but the diplomat can usually raise their opinion by a greater amount than the penalty. Might not work if your diplo ship is trespassing in their home system though; I would have to reexamine the numbers.