What is the smartest way to delete inquiries from your credit report?

You cannot delete inquiries if they had permissible purpose. They will fall off in 2 years.

Can the company that made the inquiry delete the inquiry?

We were forced to move when our landlord wanted to move back into their house.
We had found a new place to move but the details had not been completed and were looking for other options in case the deal fell through.

We had found another house to look at and they would not show it unless we filled out their credit app. I had asked two different people in their office if it would be a soft or hard inquiry and they assured me it would be a soft inquiry and would not show up on my credit report. Well it turns out they either lied or ran it wrong because it is a hard inquiry. If I had known this would be a hard inquiry, I would not have applied because this was only as a backup if needed.

I had asked them about it and their response was "I don’t understand what the problem is. We have to run your credit to make sure you are qualified to rent. We do not see your score we only see your portfolio. So we do not know your credit score just your history. There is no way to fix this inquiry when you sign the application it gave us permission to run your credit. I am very sorry, but please make sure you read the bottom of the application that you signed."

You signed for a credit app to be run...they had permissible purpose. The office staff probably doesnt know the difference between hard and soft. You are stuck with it.