You need to delete all pingbacks by going to Dashboard -> Comments and then do not approve pingbacks if you don’t want to display them. Backlinks are important, displaying them on your page matter much less. Most professionally managed blogs do not display pingbacks as it just takes up space.
If you uncheck link notification from here http://themonic.com/forums/topic/remove-comments-on-post-by-ping-back/#post-1952 you should not receive pingback notifications too.
