Like Vince said, if you have access to Audition then you’re golden – just use the noise reduction tool.
However, (also like Vince said) the sadly stripped down version called Soundbooth can do it for you too.. In fact, I just spent countless hours cleaning up the audio from an hour and a half school play where the audio guy had feedback out the whazoo and left mic’s open when they shouldn’t have been open – major lav rustling throughout the entire hour and a half.
Sorry about that complaining..
Anyway, in soundbooth, I’ve grown to like the Spectral display. For the stuff I was doing it was mostly lower frequency stuff – the mic rustling was roughly 200 Mhz or below and the feedback was about 500 Mhz. You say your’s is high frequency, but the below should work for you no matter what the frequency of the noise.
Option A:
Use the Reduce Noise ‘task’
Select an area (preferably 5 seconds but as long as possible – even if it’s a fraction of a second) that has only the noise you want to remove..
In the Tasks panel, choose Clean Up Audio -> Capture Noise Print.
Then de select (or select the entire file) and click ‘Noise’ from the same panel. It only gives you two settings so play with them (using the preview) until you are happy. Don’t go too aggressive or it’ll distort the audio and it’ll sound heavilly compressed
OR
Option 2:
In the spectral display, use the lasso tool to select an area where you expect to hear the noise (and only the noise). Select ‘Play Selected Frequencies only, select loop and play it. If you hear your sound, then you can go through at very small increments and use the ‘Auto Heal (I set my resolution to 4096 (Slow)). Or, you can select larger sections at a time and reduce the amplitude.
Either way, make sure you listen to it periodically as you go..
HTH
–KTFA