I am not sure how it would be unauthorised. Unauthorised would be if you had never went to them for anything and saw an inquiry done. If you typed in your information and were seeking a quote on interest rates, they are authorised to obtain a credit report. How else do you expect them to give you a rate? No one is going to give you a quote without looking at a credit report first.
I don't see why using them would make it seem like you are desperate for credit any more than using Chase to obtain a loan. Lending Tree doesn't actually loan money, they find lenders for you to loan the money.
As LS2982 said, it was most likely a soft inquiry since that is what it says on their page. You don't need a hard inquiry done to obtain a score.
