Modify / Delete Work Item Templates in Web Client
One answer
According to the link below, it appears that deleting Work Item Templates is a process configuration that is available on the Eclipse client.
http://www-01.ibm.com/support/knowledgecenter/SSYMRC_5.0.0/com.ibm.team.workitem.doc/topics/t_creating_work_items_from_template.html
Hope this helps