SSH – Why Change Default SSH Port?

It is not possible for them to simply hijack your connection and take over your PC simply because you used SSH to connect to their remote server. However, everything you do on that remote server can certainly be monitored. Any passwords you might type in through the remote SSH connection can be captured, but that's because you are sending that data to them, not because they are monitoring your home computer. If they hijack your PTS session, they can do nothing more than you can on their own remote server. It gains them nothing as they already have that much power over their own server. If they type exit, they will end your remote shell and you will be booted off, but they won't gain any control over your computer. That PTS session was on the remote computer and has nothing to do with any PTS sessions you might have on your home computer. There is always a chance there could be a security exploit in your SSH client that might give them some access to your machine, but if your keep your software reasonably up to date, it's extremely unlikely and I wouldn't worry about it.

With that said, there are ways to make you computer more vulnerable with SSH. If you enable certain type of forwarding, they might be able to use that against you. All forwarding is off by default. If you have agent forwarding enabled, they can use any private keys you have loaded in your agent on your home computer but only while the SSH connection is established. An agent does not allow anyone to steal keys, but they can use them as long as you are forwarding it to their server. You should never enable agent forwarding to an untrusted computer. X11 forwarding can allow them to launch applications and even take control of your X session. OpenSSH, by default does some filtering of the X11 protocol when forwarding (unless you have ForwardX11Trusted enabled) and so they can't take over complete control, but they can still load windows on your X session. Again, X11 forwarding needs to be used cautiously.