The word UNFAVORABLY only appears in one place in AR 600-8-2. It does nothing to help with the definition. My interpretation is that Unfavorably means the flag was removed with adverse action taken.
For example: Soldier receives and Article 15 for an offense. The flag would be removed unfavorably. Please see the extract below.
(b) Criminal violation. This includes violation of Title 18 USC concerning sabotage, espionage, treason, sedition, subversion, terrorist activity, deliberate compromise of classified information, or unauthorized disclosure of classified information; violations of UCMJ, ARTs 94, 104, 106, or 106a; or offenses equivalent to those listed in this paragraph alleged as violations of UCMJ, ARTs 133 or 134. When the case is closed favorably, remove the Flag and update the DOD CAF, as necessary. When the case is closed unfavorably, remove the Flag upon direction of the Secretary of the Army.