HHS/Office of Inspector General Excluded Individuals last updated checks that the downloaded exclusions file is not older than the date you set.
HHS/Office of Inspector General Excluded Individuals last run is triggered if the search process has not been done recently.
HHS/Office of Inspector General Excluded Individuals records pending verification is triggered if there are potential matches of people in your database against the exclusions file and those potential matches have not been marked as "Match" or "No match".