Deleting a custom template is easy!
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Step 1: Go to Settings > Custom Templates.
​Step 2: Select the message template you want to edit.
​Step 3: Click the "Trash" icon at the right of the template.
​Step 4: Click "Yes" to confirm.

You can use the mobile app to send messages using templates, but the message templates can only be edited from the web app at this time.