There are three ways to delete a task in TeamPulse:
option 1: Open the story; go to the tasks tab; select the tasks you want to delete by clicking on their check-boxes and click on the "trash" button to delete them.
option 2: Find the task using the global search tool: Just click the magnifying glass icon at the top right of the screen (or use the keyboard shortcut - type "s"). Type the name of the task and open it. From the "Actions" menu, click on Delete.
option 3: Create a board with rows by parent item. Select the tasks you want to delete and click on Delete from the "Actions" menu. Here is some info about configuring board rows and columns: http://docs.telerik.com/teampulse/user-guide/interface-guide/views/Configuring-Board-Rows-And-Columns
Do not hesitate to get back to us if you need any further assistance.