What's included in the letter will be totally at the elders discretion. These guys arnt trained in how to write proper letters like say a HR manager or a teacher. All it would take it one incompetent elder to spill the beans on all your private details.
In short - it depends on the elders you have. Although if i were you I'd state implicitly that you wish them not to disclose the reason for the reproof. If the matter is supposed to be settled with Jehovah then why dig it up? Ask to see the letter before it's sent.
However, whatever it was, count on it that the entire body of elders will know the in's and out's of what you did - as will their wives, likely their kids and certainly the elders wives friends. I'm speaking from experience as a former elders son in law. We knew the details about Judicial Committee's, reproves, spiritual estimations of congregation members.