The returned

"You cannot strengthen cats-eye earrings of amber, glaring alevolently."

is correct. If I understand the spirit of the skill, it is to allow you to improve the protective value of natural-materials armors so long as they can be worn like armor. That is, you could have a treasure item worn on your face and that would provide you some measure of protection. In this case, we have a treasure item worn on the ears. I agree with the code here that an item like this falls outside the realm of what strengthen was designed to do.