Letter #1: This is a simple letter:
The reason why xyz, abc, mpo appears on my credit is because I was shopping around for the best interest rate. No new account is opened as a result of the credit check. Thank you.
Letter #2: This one will result in additional information required by lenders:
The reason why (example) Chase, American Express, Home Depot ran my credit is because I open an interest free account with them. GMC ran my credit because I recently purchase a brand new car with them. Thank you.
If letter #2 applies to you, get ready to provide a copy of statements from all those creditors. Banks will need to add the monthly obligation appears on those statements into your debt ratio and determine your qualification for the loan.