There was no way to clear an old or junk chat out of the inbox, and a chat with a number that cannot receive WhatsApp looked exactly like a live one.

Archive and Delete

Each chat in the list now has an actions menu:

Archive moves the chat out of the inbox. The new Archived tab lists it, and Move to inbox brings it back.
Delete asks first. The message history is kept, and the chat comes back if the contact writes again.

A customer who writes to an archived chat brings it back to the inbox on its own, so archiving never hides a new message.

Numbers that cannot receive WhatsApp

A chat whose number cannot receive WhatsApp now carries a red badge. Hover over it to see the reason.