What are these burn marks on PCB?
What you are looking at is most likely Flux resides - the acidic compound in solder that helps it flow. Depending on the solder this can be due to too high a temperature as pointed out in the comments - though having said that 350°C is not ridiculously high for lead-free solder if the temperature control is good (many cheap irons can get a lot hotter than shown), I tend to be soldering at ~280°C to ~345°C depending on how much copper there is in the board cooling the pads (e.g. 4-layer needs more heat soak). It could also simply due to the type of flux - rosin based fluxes leave a horrible mess much like what you see.

The boards look worse than say a green PCB simply because the white shows up the mess more visibly. Having said that, regardless of the PCB colour, your best bet is to clean it up as the residues can damage the metal over time and in some cases can be slightly conductive and disrupt high-impedance circuits.

As @WesleyLee points out you can use IPA to try to dissolve the flux, however you will also need to scrub with an old toothbrush and wipe off the residues. Bear in mind that all the IPA does is partially dissolve the flux and turns it in to a gooey liquid. If you don't scrub it off, the IPA then evaporates leaving the residues behind as a sticky mess that then attracts dust and other particulates to stick.

Having recently been doing some rework (lots of flux and desoldering wick), I've had some pretty big flux messes to clean up. On these boards there were quite a few very fine pitched ICs, so scrubbing is not an option. I had some  thermal paste cleaner (this which is limonene/soybean based) to hand, so tried it.

The first step cleaner works really well at completely dissolving and flux - to the point where you can actually just gently wipe it off with cotton swap (no scrubbing). Once the flux is wiped off, you can use IPA or the second step of the linked product to remove any final residues from the cleaner.

Once the flux is removed the boards will look a lot better - it is highly unlikely there is any damage to the underlying solder mask.



It should be noted I am in no way affiliated with Arctic Silver, nor is this intended as a sales pitch, it's just the best product I've come across for de-fluxing PCBs easily.