To delete an alert that you have set up, click on the Analytical Tools menu option in TWS and select Alerts. All of your alerts will be listed on the window that populates.
Left-click on the active, blinking alert that you wish to turn off. If you wish to disable an alert, click on it and click the "Deactivate" button on the right side. If you wish to delete the alert altogether, choose the "Delete" option. Once finished, simply close out the window.
More information on Alerts can be found in the TWS Users' Guide.