Sounds like you done a sensible repair to the board.
With the best will in world PCBs don't take kindly to repeated cycles of soldering and desoldering.
Regarding your iron you are actually more likely to damage the board with a lower powered iron.
I've posted on this elsewhere, but to briefly recap, the key to good soldering/ desoldering is to heat up the joint as quickly as possible to the melting point of the solder, thus minimizing heat transferred to surrounding components/ PCB tracks.
All things being equal, a 40W iron doesn't reach a higher temperature than say a 12W iron, however a 40W iron can deliver more energy to the solder joint with cooling itself, so you can heat the solder joint more quickly, and hence reduce collateral damage.
The problem with lead-free solder is it's higher melting point, typically 227 deg C, but can be higher, cf around 180 degC for leaded solder.
The necessitates the use of a higher tip temperature; I use 430 degC forlead-free work cf 370 degC for leaded solder. Obviously this increases the chances of collateral damage somewhat, however trying to melt lead-free with an iron designed for leaded, and hence lower temp, increases the likely hood of collateral.
