Mike:

You can't delete the first date, all you can do is remove the numbers from each column.

From the first date field tab into the second so that the date is fully highlighted then press the delete key and finally select Okay. Should be gone. Don't forget that this information may be stored in multiple locations, you have to delete each one (though you should be able to delete a single location and not see it in that location any more).

Looks like this might be an issue for your Adagio consultant to help you out with.