It took way too long and too many phone calls and letters, but I'm glad to report the successful removal of a hard INQ that had been reported with no apparent permissible purpose. The details are available in this earlier thread , but in summary:
An INQ turned up mysteriously on my TU report a few months after closing a mortgage refi. After lots of investigation, I determined that the party requesting my CR was a fourth-party "reseller", collecting information related to my mortgage origination for a third-party "mortgage auditor", and that these audits are required by Fannie/Freddie on 10% of every lender's loans.
Nothing wrong with most of this (as far as I'm concerned), except that I considered the hard pull unjustified and improperly derogatory. I had not applied for, nor received, any additional credit, and the long delay meant that it would not be aggregated with my mortgage apps. Nevertheless, everyone at all the entities I contacted about this assured me that "the CRAs all insist" on the hard pull (except that TU themselves refused to say anything about it at all), and that the reseller had inherited permissible purpose for this INQ through a document I signed at the closing.
I thought it would be worth a try to challenge that last point. I wrote to the fourth-party reseller listed on my report, asked them to investigate whether their client, the third-party auditor, had PP for a hard pull, with specific requests for each of two possible outcomes. If their investigation determined that PP did exist, I requested details including the name of the organization that originated the INQ, and contact information for a person who could confirm and explain the PP. OTOH, if they could not establish PP, I requested that the inquiry be removed from my CR.
I recently received their response: "We have requested that the inquiry be removed from your credit report"! I waited a week, checked my TU report, and yes, it was gone. Path of least resistance, probably, and just a small victory, but better than nothing.
Starting Score: EQ 804 - (April 2009) 
Hey, WHATEVER IT TAKES 
Well done
@DallasLoanGuy wrote:you must have a lot of time on your hands.....
what was the effect on the score? like 2 points?
I don't, actually. I just hate getting a ding I don't deserve. I'm careful about what I apply for, and this limited my options. And when I started this process, there was always the concern it could be a red flag for fraud.
No discernable effect on the score, but I didn't expect any. The process took long enough it dropped out of the one-year score zone anyway. But there's more to credit than just scores. Mainly, I didn't want some analyst with one of my existing accounts wondering what I'm up to.
So was the information about mortgage audits that I received and summarized accurate? I hoped you might know.