As long as you have the "Edit Plans" permission listed under the "Task" section you will be able to delete tasks. If you don't have this permission, update your security roles to make sure it is included and then log out and back in for those changes to take effect.
You can then delete a task by accessing the project plan that the task is associated with and checking that plan out. Then just right click on the task you'd like to get rid of and click "Delete Task". This action will be reflected across the system and that team member will no longer see the task in their assignments.
Let me know if this helps and if you have any other questions.