Credit inquiry for mortgages hurt my credit?

My fiance and I are currently shopping to refinance a mortgage on the home we are in. We went to the first bank and when they pulled our credit we were told that we had 45 days to shop around, and that within the time frame a mortgage company could pull our credit without it effecting us.

We went around to five banks and filled an application with each.

The issue is that each of those banks pulled our credit at least once (three of them pulled it twice) and every single time we took a hit to our credit score.

Before this process started I was over 720 which was reported as “great” credit and from these inquiries alone I have dropped 26 points. I am now very mid range “good” credit.

What is going on? Was this supposed to happen? Why am I being punished for being responsible and proactive enough to shop around?

Is there any way for me to dispute any of this with the invisible algorithm dictating our livelihood and interest rates?

Edit: I’m very impressed with the amount of help I received and how quickly I received it. Thank you for the clear and honest answers and links to previous comments/wikis. I appreciate it all. This is probably the most helpful post I’ve ever made. Good job on this sub.