This letter is as much about using the Casio name in sales as it is about the sales themselves, it seems.
So it gets into multiple areas of law: trademark law (The Casio name is certainly a trademark), FDA-related radiation control law, etc. If you indeed do fall under the FDA's definition of a manufacturer in your extraction/reselling activities, then point i) on the letter is valid.
Remember there are multiple different facets of intellectual property law, and they all mean different things. Copyright law, trademark law, patent law are all related, but are all different. I believe the foremost of Casio's concern with that letter is trademark.
But I think Casio's lawyers sent the letter mostly because of point ii). They clearly think i) is a problem as well, but the real reason they wrote the letter was what they said in point ii). Using Casio's name in ebay sales of these diodes is definitely a problem, and Casio has every right to stop that practice.
So if you want to sell the diodes extracted from the projectors, definitely leave any association with Casio out of it completely.