What model is it? The first Ultegra 9-speed brifters (6500) had a chronic rattle from the face plate and Shimano made a design revision to quiet them down (6510).

There was a technique to remove and shim the face plate but I don't have a reference to it. Perhaps a Google search will find it.

If it's a 6510 or newer, was the lever removed from the body at any time? There is a return spring in the lever and, if it was left out, the entire lever can rattle.