New Cafe World 'remove neighbor' button boots undesirables
To delete a neighbor, load Cafe World and then click on the 'Neighbors' tab at the top of the page. Once on the Neighbors page, scroll down the page -- below the big 'Find Friends' module until you reach another module that looks like the image below.
This list should contain all of your existing Cafe World friends. To delete a neighbor, simply scroll until you find their name and click the red 'Remove' button next to their name. Congratulations -- you've successfully eradicated any unwanted neighbors.