Plugin “index.core.php”

I just found new users added to my blog and am in the process of following some steps to secure my site against hacks.

In looking in my plugins on my dashboard, I noticed one that simply said “Deactivate” with no title or details. The Hello Dolly one was back also after having deleted it a couple months ago (when I was having similar issues) In my cPanel File Manager plugins file there is a file that says index.core.php.

Can anyone tell me what this is and if I’m suppose to have it? Can I safely delete this?