This feature is only available in STANDARD and PRO package.
How to block a visitor?
If they are still on your website, block them in the conversation, click on the menu icon (1) and after that select block visitor (2). You can unblock a visitor the same way. The chat will disappear for the blocked visitor.
Block IP address
If you know the IP address of this visitor, it is possible to block the IP in the Settings (1) → Account settings (2) → Security and privacy (3) → Add IP address (4)
Tip: You can use asterisks (*) to block a bigger range of IP addresses. Some examples: