Hi Justin and all,
The whistle is the injection tone used for descrambling that should be balanced out of the audio output but isn't due to an imbalance in the mixer circuit. OK, you don't know what I'm talking about so just accept the fact that somewhere along the line one or more components is out of tolerance.
Lord J has a good idea, a software or hardware digital signal processor (DSP) is just a bit more than you need for this application though. Specifically you need a notch filter to remove the tone and DSPs have them so unless you're processing audio for more complex applications the simplest one available or a stand alone filter will do.
Now I'm kicking myself, a while back I lost a good software DSP when I lost a drive (too recent an addition for current backup) and the download page where I got it went with it. Sometimes serendipity can be painful but if you join me in searching the Internet maybe someone will find it. While you're at it maybe you'll find a good software voice inversion descrambler and chalk up Ramsey to a learning experience.
When scrambling first came on the scene I built a scrambler/descrambler from scratch and it worked perfectly. Well, ya does whatcha gotta do when no kit is available and Ramsey wasn't even an idea yet. Hmmm, could be there's a schematic floating around in cyberspace for you solder smoke junkies.