Samantha, I don't believe there is a way to delete readings. I've just looked through the settings of my own, and can't find anything. I haven't looked in the Professional Options, as I can't recall the password, but I seem to recall when I looked in, when I first had the Libre, it didn't hold anything too beguiling to me.
I wonder if @tim2000s or @robert72 would know the password to allow you to look. (Sorry to tag you guys.)