Heh, interestingly enough, gold platings (at least as in ENIG; you should rarely if ever need to solder hard gold (>30u")?) dissolve almost instantaneously at normal soldering temperatures; I suppose they may well survive for a moment at lower temperatures, making that a possible failure mode.
The traditional solution is to tin and wash the joint -- just as you do with the tip as described above. Same as rinsing in any other chemical process: fresh solder is your solvent and sponge and wick are your towels.
BTW, main downside to leaving indium or regular solder in the joint, is that it ends up frosty -- the alloy is far from eutectic so some part crystallizes out first, leaving a bumpy surface. The solder also takes longer to solidify (eutectic hardens as soon as it crosses solidus temperature). Uh, unless there's some creepage or corrosion problems with small amounts of indium in conventional solder, Idunno, but again as mentioned, it should be well enough washed away not to be a problem.
One possible gotcha is, standard rosin isn't very active at those low temperatures. Low melt solder I think usually comes with, or suggests, a more reactive flux for this reason. So just use that and you're fine.
Tim