To delete neighbours you already have:

(1) Go to the "Social" screen
(2) Go to the "Neighbors" screen
(3) Tap "EDIT" at the tome of the "Neighbors" screen
(4) this brings up a button by each neighbour "REMOVE". Tap the "REMOVE" button for the neighbour you wish to delete.

Now if the problem is deleting neighbours you've sent out invites to, but they've not accepted (or declined), you can't do this. You're just stuck with them on the pending invite screen.

Hope this helps.