Luckily, I came across a forum thread that gave a solution for this annoyance.
"KSH Terminal Settings"
http://www.unix.com/unix-dummies-questions-answers/25310-ksh-terminal-settings.html
What I found out was that I could start the SSH session and then type the command
stty erase ^H
, which would enable me to delete correctly both within the SSH session and in my native Mac OS X Terminal after I ended the session.The only (possible) problem is: Now that I've changed the erase character on the server, it appears to have "stuck". So, I hope other people who are accessing the server don't suddenly find that their backspace keys have now stopped working...