My understanding is you will never see the remnants of an old hamon on a re hardened sword, as before a new one is created the blade is heated and allowed to cool naturally. This removes the old hamon, both functionally and visibly. (I think this is also when the grain takes on the looser and glassy look,from multiple expansion contraction and change in carbon content)
From the photos it just looks like the polisher didn't consistently follow the hamon, so the peaks aren't as white as the the rest when using hazuya finger stones,
http://www.ksky.ne.jp./~sumie99/utsuri.html
As an aside, maybe I just haven't seen enough swords or my logic is faulty, but I don't think there are as many re-tempered swords out there as people believe. It seems to me any swords that were really important and worth the effort are already very rare, (for example blades made by Koto masters damaged in a fire that were given to Echizen Yasatsugu and re tempered for the Shogun)
Any munitions grade swords for ashigaru or even mid level blades were probably scrapped, and not worth digging through the rubble after a castle fire, and any that were reworked during a campaign due to battle wear saw attrition through just being used up.
Regards,
Lance