Clicking any soft of message in the legacy version of the Web TeleConsole does not provides any deletion option.
When you click a chat or a text message it will open the related conversation.
When you click a voicemail it will open the playback window for the message and the same is true when you click a fax, which will just open the fax document.
Once you make a selection, a Delete button, counting the number of items you selected, will appear at the bottom of the window. Click it and you will be asked to confirm the deletion. Or click the Cancel button next to it to deselect all the items.
You can delete sms/chats messages, voicemails, and faxes at the same time from the All tab.
One more option for voicemail deletion is from an email you receive if the voicemail-to-email option is enabled in the TeleConsole voicemail notification settings.The email contains a clickable link that deletes the related voicemail.