What ended up resolving the issue was pressing ctrl-alt-del on the remote machine to bring up the help/lock screen, and that was it! Just from that, I regained full control both locally and remotely. Turns out, I had no input control on that machine - not keyboard or mouse - even when I had ended the Tv session. In my case, I use Tv as a mere lazy convenience to access a machine in another room of my house so, after discovering this issue, I just decided to see if there was anything wrong on the remote machine itself.
I tried checking through multiple options, particularly "disable remote input", and nothing worked. I just ran into a similar problem a few minutes ago: I could interact with the remote machine with my mouse, but all keyboard input remained inactive (this is the first time I have experienced this issue with Teamviewer). This is actually more of a response to this question, but I thought would still be relevant here.