A lot of chickens will eat an egg that is opened, say it breaks accidentally. That doesn’t make her an egg eater. It’s when she’s opening them on purpose that it’s a problem. Accidentally broken eggs is one way to get them started. An egg eater can teach other hens to open eggs. That is not a good situation at all.
I agree that egg looks pecked. Something else that can cause damage somewhat like that is a nail sticking up in the nest or maybe a hen stuck a claw through it, especially if it is thin-shelled. But with the depth of that hole, it looks pecked.
How attached are you to your individual hens? I had an egg eater once and as soon as I found out which one it was, I ate her before she could teach the others. But I mainly raise them for meat to start with so that decision was easy.
Other people will tell you of various techniques to retrain an egg eater. I haven’t done any of them so I can’t say how effective any of those are. One way that can work is to build a roll-away nest. When the hen lays the egg it rolls out of the nest into an area where the hen can’t get to it. That would not work for me since I want my broody hens to be able to hatch with the flock, but maybe you want to consider it.