If you realize that there was a mistake in a saved race (say a missing lap time or to remove a person that didn't run) and you wish to correct it, it's easy. While viewing the race in History, tap on the title of the race at the top of the screen and tap on Make Current Race. This will reload the old race as your current one and you make any changes you wish.
Note that the previous race is unaffected, and can be made the Current Race at any time. You can even do this while the race is running and switch back and forth.