Sorry, you won't be able to do anything with that audio at all. No recording can ever be 'undistorted' after it got itself distorted in the first place, simply because there's no reference to what it should have sounded like to work with. What it amounts to is that no recording can ever be made 'better' than it is originally. You might be able to reduce noise, get rid of background sounds, make it louder, etc but actually improve it - well I'm afraid you simply can't.
In this case it's even worse because it's been gated to get rid of background noise, which has also cut off many of the start transients, which makes it even harder to hear what's been said. And that you really can't do anything about restoring them - they simply aren't there!
In this instance I'd complain to the course provider, and see if they have an original that hasn't been compressed, gated and distorted so much. I agree with you about the quality - I wouldn't want to listen to very much of this either.