Select all Found records
Then Click on Mass Edit
Tick the Internal Contract Owner field and next
Search for the new person/owner by clicking on the mirror icon
This page will open. Type the new person’s name Go click Select
Lastly click Finish with below option ticked. It should run through and update all records replacing the previous owner with new person
When changing the Contract Owner, you don’t need to tick Run Rules, but can always leave the Update Defaults checked so it updates the date/time of the edit and the person making the edit.