A quick search reveals only a little. The author explains:
"... analysis is run on source content to indicate need for apodizing filter. As such it is just an indicator to tell you when you need apodizing filter to correctly reconstruct the source content. If it stays at 0, you don’t necessarily need to use apodizing filter, but there’s no harm at all still using such.
So the sound quality improvement is only through your choice of filter based on the provided information.
It is counter to indicate how many times HQPlayer has detected certain types of distortion inducing errors in the source content. Latest improvements make it more accurate and reliable."
Like you, I wonder if "distortion inducing errors in the source" means data that reconstructs to above full scale. Would an apodizing filter deal better with that? I haven't ever thought about that issue.
My tests here a couple of years ago failed to persuade me that different filters did anything significantly different. However that was on classical music (and a small amount of jazz) and I suspect largely recorded so that true peak stays below FS.