(...)draw the chits determined by the target card, "No Site" chits are removed(...)
In the pdf version of HL2 there are no No site counters. There are only No bandit ones and you may only place bandits at the end of the Target-Bound Flight phase.
As it's a pain to try to remove all the SA-15s on VASSAL, I presume I should instead remove any SA-15s that appear and draw another chit for each one removed.
There shouldn't be any major problems playing this way as long as it's still a random chosen counter on the next draw. However, there are 4 SA-15 counters with 3 MiG-21s and 1 MiG-23 on their backs. If, when determining sites, you remove any of the 4 SA-15s from game you won't have the same selection of bandits at the end of the Target-Bound Flight phase. Just put them back in the cup (or the VASSAL equivalent, if any) and use them again for their bandit side later in the game.