I'm on MS office 2013. I need to uncheck the "Trust access to the VBA project object model" check box for some testing purpose. But I'm unable to do so, as it is greyed out (and it is checked).
What might be the reason. How can I enable the check box?

According to Plan security settings for VBA macros for Office 2013:
You can check this article for how to change the Group Policy.
Summary:
gpedit.msc, and then choose ENTER.In your case, look for
Disable VBA for Office applications.