With our Team Plan, the admin is able to export chats into a CSV. It's easy to do -- just go to Administration on the left-hand side of the web app, then select inbox you want to export chats from.
Click on Export Chats at the bottom, and you will be prompted to select the date in which you'd like to export chats from. Current chats from the current day cannot be exported.
Select the date range you want to export and decide if you want to export chats individually or all in one CSV then click on the yellow Export button on the bottom-right.
Once the export is complete, you'll see a clickable link next to the Export Chats link. Clicking on that will download a .zip file with the CSV contained. You can then upload that CSV to your preferred spreadsheet management system to review.