At the moment with the BlurEffect it is impossible to blur just one region of the screen. Prior to having the blur effect, people were using neon parts which snapped to the camera’s view to create a similar effect. It’s not It wasn’t a perfect blur, but in The Conquerors 3 you can see used to be able to see BrokenBone’s lobby looks like it has looked like it had blurred GUI elements. He is was using a Module3D script to lock a neon part to the screen to fill a space.
I have personally never used a Module3D script so I can’t suggest any, look around and there are some great tutorials out there to use them too, or even to create your own.
Edit: I found this one by TheNexusAvenger, there’s some documentation inside of it. It appears to be the most up to date, public version I could find.
Edit 2: Updated for correctness as people still refer to this. Also, since future is bright’s neon update, darker colors that previously used for a blur effect no longer have the same effect. You can now only do this with a lighter colored blur.