Let me start by saying I have absolutely no experience with those overflows. Mine is a through-the-back overflow from glass-holes. So I'm not sure this would work for the HOB ones or if it would interfere with it in any way (my little disclaimer).
That being said, mine was super noisy at first - the water pouring into it and then down the drain. The company that made the overflow recommends this enkamat stuff:
Enkamat - you can buy it by the inch at that site as well.
It is basically a super open weave of nylon. What it does in the overflow is greatly reduce that splashing and flowing noise. The weave is open enough that it doesn't impede water flow (unless you never clean the stuff and it gets super nasty). If your overflow is clear, you could probably do some just as a layer on the bottom, so that it is kinda cushioning the water flowing down - I would be afraid if the box is clear, then the enkamat would be a great media to grow algae on and would clog for sure if the box was stuffed with it, but an algae covered layer at the bottom of the box shouldn't hurt anything. If the box doesn't get light in it, you can stuff a bunch in the overflow as the water just flows through it anyways and it can't grow algae in the dark (this is what I did).