There are several ways to delete an alert.

  • Alert that is shared with me and within my quota

From the feed, next to your alert's title, click on the Edit icon:

On the next screen, you'll get the ability to delete the alert:

  • Alert that is not shared with me or that's exceeding my current quota:

If you want to delete an alert that is not shared with you but used by a different team member, you have to make sure you're an Admin.
 You can then click on the Settings / Quota page to get an overview of all the alerts that are active on your account.
 If there's a colored dot next to the alert's name, then it means that you already have access to the alert, which can be edited or deleted.
 If you only see the name of the alert, you have the ability to join it and you'll then see a colored dot too.
 
 Once you have access to the alert, you can click on the trash icon to delete the alert, either for yourself or for the whole team:

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