Inviting someone outside your team to Walkie Talkie now sends the same invitation as any other guest: they join as a guest of your Personal, with their conversation with you and nothing else, and are listed on Personal's guests page. An emailed invitation also waits on Your teams for someone who already has a Magpie account. A link can be used by several people, and each gets their own conversation with you.
Replying to a message from your talk page makes its sender a guest of your Personal in the same way. A channel's invitation link makes the people who use it guests of the channel's team, with that channel only; guests are never in a team's channel for everyone.
A direct conversation stays open while the two of you share a team where both of you use Walkie Talkie. When you no longer do, it becomes read-only for both of you, with Invite as a guest to carry on.