Unpair remote from ipod universal dock?

I finally figured out a work-around for this. Pair the remote with the dock (hold Menu and FFWD for 5 seconds while pointed at the dock) then increment the remote ID (hold Menu and Play for 5 seconds while not pointed at an IR receiver). Then, you can pair the remote with its new ID with your Mac, without affecting the iPod in your dock.

Note that pairing the remote with something does not prevent that remote from controlling other items.
It simply means that the one item can only be controlled only by that remote. The remote will still control other items unless they are paired with a different remote.

http://docs.info.apple.com/article.html?artnum=302782
“To reset the dock to work with all remotes

1. Make sure other products that are compatible with the remote are powered off.
2. Connect the dock to your computer or to an electrical outlet.
3. Put an iPod in the dock and turn the iPod on.
4. Point the remote at the front of the dock.
5. Press and hold the Menu and Previous/Rewind buttons together for about six seconds”

This didn't answer my question.

So the instruction on how to unpair it from the dock and the link for the same which I posted above is not what you are looking for?

I don't want the remote to control the dock anymore.

As I wrote above, the only way you can have your remote NOT control the dock is if you pair the dock with a different remote. Or cover up the sensor.
Unpairing it will not prevent it from controlling it. Unpairing it means that all remotes (even the one you now have) will control the dock.

I know you can unpair it with the computer, so I was hoping you could do the same with the dock.

You can. Follow the instructions I posted above.
However, doing that will not prevent the remote from controlling the dock.

When you pair a remote with a dock or a computer, it simply means that the remote it is paired with is the only remote that will control it. It does NOT prevent the remote from controlling anything else.