Do you have a link or reference where you got the circuit from? The reason I ask is because the feedback amplifier looks like it produces a current output and VGA3 presumably doesn't have a low impedance voltage output otherwise the circuit wouldn't work. An explanation of the circuit requires some knowledge of the internals of the amplifier blocks in this case.
While you talk about DC offsets, the fact that it uses a low pass filter means it will track changing offsets. As the LPF in your example is 500kHz then it will track fairly rapid changes in the offset. You would normally want to keep the LPF well away from the signal of interest otherwise the DC correction will try to remove the signal as well. The signal in your case is 2.2GHz - well away from the 500kHz.
So, in a simpler example, like the one I gave, a filtered, inverted version of the output signal is added to the input signal to cancel out the offset. The same thing is happening with your circuit, but it is more complex because it is fully differential and a current output error amplifier is used.
The output of a low pass filter when fed with a very high frequency (well above its cutoff frequency) is the "average" of the input voltage.
I am not sure if I have helped much.
Keith.