The JD in the signature of that kind of letter usually amounts to more weight than the content, regardless of whether the wording was perfect and the research duly diligent.
In this case, it refers to the literal letters written in the signature of a letter, which presumably indicate that whoever wrote it studied a bunch to get into school, paid a bunch to go to school, graduated with that degree, and should be respected, because they may have the knowledge, willingness, and resources to take the words in the letter further, if they want to, given that they have already somewhat attached themselves to the cause in the form of the letter.
[0] https://law.stanford.edu/office-of-student-affairs/the-docto...