This box of eye shields has nothing on it that would indicate the manufacturer. Nevertheless, it appears identical to the ones manufactured and advertised in the early 1940s by Mager & Gougelman, Inc. of Chicago Illinois. The Radium Chemical Company of New York appears to have been one of the distributors.
Quoting a 1942 advertisement:  SAFEGUARD YOUR PATIENTS" EYES - with Gougelman Protective Eye Shields . . . nickel-plated lead cups, they permit Radium and X-Ray therapeutic head treatments without danger to the eyeball or delicate healthy tissue."
Other literature indicates that they were silver plated or simply "plated."
The manufacturer's literature claimed that "at 140 KVP with 1 mm aluminum filter the radiation does not exceed 2 % of the impinging beam."

The second photo shows (left to right): the outer shield, the inner shield and the outer locater shield.  The outer shield fits over the eyeball and lid to protect them while treating the surrounding tissue.  The inner shield fits under the lid. Used alone it protects the eyeball while treating the lid. The outer locater shield used in conjunction with the inner shield is placed over the lid with the aperture exposing the lid area to be treated.    

Size: approximately 4.75" x 3" x 1" case