No the teak won't rot
away. You can leave it like that and all that will happen is the mold
will spread, teak does not usually rot.
It does sound like they did not allow the morning dew to dry off proper before starting the first coat and moisture was trapped in the finish. So sorry newt, the only fix is to start over. Heat gun is ok, since it is compromised, should come off nicely. Use a fresh scraper, sand to round the edge of the scraper blades to protect from accidental gouging of the wood.
Please no bristles on the wood to get the mold
out. Just get the bad two part finish off, lite scrub with a 3M pad ( white 3Mpad or sponge is best) and Tide with bleach ( powder), and then a nice salt
bath, give her a day or two to rest and see what you have.
When and if you are ready to put a finish on her.
Wash her down with big sudsy bucket of murphy's oil
soap and fresh water
, let wood dry overnight.
wipe down with denatured alcohol after dew has dried
light 320-360 sand if needed ( I'm assuming the previous workers got the wood properly smooth) this sanding is just to address the grain you raised from washing/ water
Wipe again with denatured alcohol and then a tack rag
Tape off area or use painters edge
Start your first coat of whatever
Sorry for your troubles,