Importance of wicking during rework?
Applying new solder on BGA packages with plain soldering iron is not the right technology. Both the IC pads and PCB pads should be thoroughly cleaned from excess of old solder, totally, to have planarity/uniformity. That's why the solder wick is important. Then a specially manufactured balls of solder should be applied to BGA, of proper size,



which is called "re-balling". Then the IC should be aligned with PCB pads and re-flowed in standard way, either in hot-air station, or IR-heated soldering station. You can't apply new solder bumps with simple soldering iron, you won't be able to make the bumps uniform enough to guarantee connections for all balls.

There are companies who provide "pre-balled" arrays of balls instead of placing each ball under microscope, here are instructions, Simple BGA Reballing.