Buildkite has improved its invitation email process by allowing any email address to work for invitations, whether or not it is linked to an existing account, thereby simplifying the process for both the inviter and invitee. Drawing inspiration from Basecamp 3, the emails are designed to have the reply-to address linked directly to the sender, with the sender's identity clearly displayed, along with a picture of the inviter. Additionally, Buildkite has integrated automatic email verification into the invitation process, reducing the need for separate verification steps. These changes aim to streamline the process of inviting teammates by minimizing email clutter and clicks, allowing users to focus on more critical tasks like building pipelines or engaging in leisure activities.