Whether positive or negative, in game terms background
count reduces a character’s Magic attribute by its absolute value.

Adepts that suffer a reduced Magic
attribute temporarily lose powers as
a result; the player must choose 1
Power Point worth of powers to be
nullified for each point of Magic reduction.

Filtering
Prerequisite: Cleansing (p. 55)
This advanced form of Cleansing allows an initiate to weave
a construct of temporary disruptive energies around her person
using her Counterspelling skill. This temporary astral construct,
called a “weave,” dissipates the normal warping effects of positive
background count (and only background count) on ambient
mana, effectively filtering it into a neutral state. The magician can
then tap this “purified” mana to power her spellcasting, ignoring
the usual interference of aspected background count (p. 117).
This technique may be applied against the effects of domains and
mana warps, but not mana ebbs or voids. The filtering effect is
localized and normally not perceivable on the astral plane when
used in an area saturated with background count.
To use Filtering, the character takes a Complex Action to
perform a Magic + Counterspelling Test with a threshold equal
to the local background count minus the character’s initiate grade
(minimum of 1). Note that background count does not affect the
character’s Magic for this test. Each net hit temporarily reduces the
effective background count for the initiate by 1. The filter operates
for (Magic) turns before becoming “clogged” and collapsing.

I also thought about this question, but there is no official answer up to now. The line "This temporary astral construct,
called a “weave,” dissipates the normal warping effects of positive
background count (and only background count) on ambient
mana, effectively filtering it into a neutral state." implies, that also your adept powers should be "saved". If you are in a bubble of clean mana, why should they be influenced?

According to RAW, you can ONLY filter or cleanse domains and astral hazing is a domain....so you should be able to do so.

The line "This temporary astral construct,
called a “weave,” dissipates the normal warping effects of positive
background count (and only background count) on ambient
mana, effectively filtering it into a neutral state." implies, that also your adept powers should be "saved". If you are in a bubble of clean mana, why should they be influenced?

Whatever the ambient mana conditions are , the character always stands at the heart of a Rating 4 background count (see p. 117, Street Magic)

The following quote leads me to the conclusion that you CANNOT Filter/Cleanse the BGC of Astral Hazing. It is a NEGATIVE QUALITY for a Reason, after all.

And though the normal Background Count of a Domain can be Cleansed/Filtered, Astral Hazing is not a Normal Condition.
Just my Two Nuyen...

There's nothing wrong with working around or otherwise alleviating negative qualities. The negative aspect is maintained in the efforts one has to make and initiating is quite an effort to go to.