You have to wonder if this part was approved by a qualified lawyer at all. A trade secret would describe proprietary knowledge of how to implement the technology, but would have no protection under patent law.
You definitely don't need to cite the legal justification for every demand you make in a demand letter.
You don't even need to have a valid justification to make a demand in a demand letter... it is common and normal to make arbitrary demands... they are negotiations.
https://www.wipo.int/en/web/trade-secrets#systems
Now yes, they're fair game for reverse engineering, but that doesn't mean someone can't be mad about it and tell you not to do it.