Nailed it!!!
As soon as I read your post, it made me remember an issue I was going to report but forgot about. It's issues with the intelligent gate and the Global Gate threshold. I use the classic gate in my Axe-Fx II because the intelligent gate always made strange noises on the tails of notes and the same thing happens in the Axe-Fx III.
@FractalAudio
The issue with the Axe-Fx III is that when you change the Global gate threshold, you can't hear the change until you exit the menu and if you're using the intelligent gate, the change won't be heard until you go into the Layout and the IN block. You don't have to make any changes in the IN block, you just have to go into it and the strange noise goes away.
Here's how to reproduce the noise issue:
* Select Factory Preset 04 Deluxe Verb or 06 A-Class 15 or any clean to low gain amp that has the Intelligent gate in the IN Block
* Turn up the global gate threshold all the way
* Play guitar and you won't hear any change
* Press HOME and play guitar and now you'll hear the noise
* Set the global gate threshold to 0
* Play guitar and you won't hear any change and the noise will still be there
* Press HOME and play guitar and you'll still hear the noise
* Go into Layout > Select IN Block > Press EDIT
* Play guitar and noise is gone