I cannot seem to figure out where to change or manage the images that display in the parallax background for that affect. Can anyone tell me?

I noticed that when I go to the template editor and select the Options tab there is a section called "Template Specific"... this is just blank. Should something be there?

By parallax I presume you are referring to the "Add beautiful parallax sections for announcements & news.", right?
The parallax is a module, mod_k2_content, Parallax template. It uses the item's image for the effect. You can choose a specific item for this.

The tab Template specific doesn't contain anything by default so you have nothing to worry about.