The technical answer, if you are so inclined to go through the process....
To dispute the accuracy of a credit inquiry, it is necessary to challenge the permissible purpose offered by the inquiree.
When a party makes a request for your CR, they must, under FCRA 604(f) and 607(a), provide a certification of their permissible purpose, identifying the relevant portion of section 604 upon which they assert a permissible purpose. That is a self-certifying process, and must be obtained by the CRA before they provide the credit report.
While the CRAs are charged with responsibility for ensuring compliance with sections 604(f) and 607(a), if they get the self-certification, they provide the CR.
To challenge the permissible purpose, one must get a copy of the certification provided by the inquiree and determine if the stated purpose is in fact justified.
To get that information, one could file a request with the CRA under FCRA 609(a)(1) for a copy of that certification. 609(a) requests cost $11.00. Then you have evidence to support a contention of a non-permissible purpose.
You could file a dispute with the CRA under 611(a), but without knowing the stated basis for the inquiry, how would you assert that it is inaccurate? You can guess at their probable permissible purpose, but that's usually just a guess. Since the CRA is the one who granted the request, they are most likely going to rely upon the self-certification provided to them unless shown to clearly be inaccurate.
By the time all of that goes around and comes around, FICO is most likely no longer scoring it.
The hassle over handling disputes over credit inquiries is generally considered to not be worth the effort, to the extend that the implementing rules for the new direct dispute process specifically exempt direct disputes relating to inquiries. You can only go through the CRA, and not directly to the inquiree.
