Can anyone explain the reflex wings used in powered paragliding?
I'm haven't flown them but am very familiar with them and the reflex wing controversy because I was interested in getting into the sport (I normally fly power and gliders).

A reflex wing when in "reflex mode" offloads the aft part of the wing and shifts the pressure distribution forward.  Effectively, the rear part of the wing is being allowed to "trail", or partly trail, up and not do any (or much less) work.  It's a bit similar to gliders with flaps that have a reflex setting, where the flap is angled trailing edge up a few degrees for high speed penetration flying, which off loads the trailing edge and moves the wing's pressure distribution forward and makes it behave as if it had a narrower chord.  

It's not related to reflexing flying wing aircraft trailing edges for pitch stability, where the trailing edge provides downforce in place of the absent tail; that simply can't work and isn't necessary in a paraglider.

The effect of reflex is to somewhat reduce the effective wing area, increase the effective aspect ratio, and reduce induced drag in the process.  A 26 sqm wing becomes effectively a 20 sqm wing (I'm just picking numbers here) with a narrower chord and what amounts to some loose fabric (the unloaded trailing edge) trailing behind it.  Because the TE is unloaded, you can't use the normal trailing edge drag brake steering and have to use "tip steering" controls.

The different pressure distribution increases the inflation pressure at the front of the wing and makes it more collapse resistant, and this is one of the reflex wing's selling features besides slightly higher cruising speed.  The downside is that when they do collapse, they do so violently with way more altitude loss and if you are close to the ground your wing will pretty much fling you into the dirt like a rag doll if you get a collapse.  I don't believe there are any current wings that can meet EN cert requirements while in reflex mode.  This means if you value your life you don't use reflex below a recoverable altitude, say 500 ft.

Having researched it a lot myself and noted the same thing you did, only a 5 kmph benefit, I'm not keen on reflex myself, especially after watching videos of how they behave when they collapse.