From my experience it seems that if a user empties caches (Develop menu) and delete other data twice,
the removal sticks.
About Screenshots:
I use built-in "Wave" desktop picture, Markup feature and TextEdit.
https://support.apple.com/kb/PH19143?locale=en_US
Back to HARBOR FREIGHT and Badgeville:
We can check a website page for the website data it is going to store in various folders
using the "Inspect Element" tool Safari provides.
Right/control click on a page and choose Inspect Element menu option from the contextual menu.
An Inspect Element window will open at the bottom of the page.
Click the "Storage" tab in the toolbar..
If you don't see the Storage tab, click the "+" button to reveal the options bar and select "Storage".
Click "All Storage" button in the left sidebar and go through the list.
Apple Support Community page:
You will se Badgeville listed.
To dismiss the window, click the "X" button at the top left corner.
Harbor Freight page:
You will see that in addition to "harbor freight", data from Akamai and "add this" stored.