Just a guess, but it appears you've got a calendar being poked. As for the "OPTIONS" request stuff,
this post by cPanelDon should prove useful.
Doesn't matter much, IMO, unless the site is locked out of public view. If it's accessible via a browser with no password protection, anyone can find it. For example if you were running an out of date calendar script on your site and in the footer of the page was the version # of that calendar script, it can be googled and found quite easy. And attacked/exploited in seconds.
From your screenshot I'd start with that calendar.
GL!