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I don't know that it is impossible. Never heard of it though.
How many do you have and how old are they? They only affect score for 1 year and don't hurt that much, IMO.
I have had success in getting some removed BUT I DID NOT DISPUTE THEM!
If you have an INQ that resulted in a denial you CAN send them a letter asking for it to be removed.
Dear so and so,
On 3/31/09 I applied for a credit card with your company and was denied, since my application was denied would it be possible for your company to remove the inquiry from my credit reports.
The worst thing they can say is NO
This will not work for inquiries that result in approvals. (tried that LOL)