With that said, I have personal experience with trademark law in the US (not the UK), and I don't think they have a leg to stand on if US and UK law is the same with respect to trademarks. For example, in the US, one must have a product and product literature publicly available and in use for at least one year, and one must register for the mark(s) with industry/ product -specifically noted. From the redacted letter, it appears this company is claiming to already have been granted a mark, so this should be a matter of simply looking it up.