Unable to backup/export/access an SMS conversation on Android
I have finally found a solution to this issue. Rather than repeat what's already been written very clearly and concisely, I will just refer to the URL:


  http://blog.shvetsov.com/2013/02/access-android-app-data-without-root.html


This provides a way to get access to the SQLite database that Textra uses, and export it to a computer, without needing root access. I am sincerely grateful to the guy that posted this! Potentially saved me from serious legal consequences had I been unable to access this information on my phone.