Now, I have found that this is due to the alternate character set becoming active, and echoing ^N fixes things. In the shell.
Inside tmux, though, apparently the alternate character set remains active.
Since tmux uses a pseudo-terminal for itself, I tried echoing ^N to this particular device, hoping this would reset the character set for tmux too, but it didn't work.
Any idea how to reset the character set for tmux itself?