They can cross the lake towards the forested area as long as the area is within Thorne's borders. Since this is earlier in Week 1, they'll likely find the same signs that others have spotted regarding the symbols and withered wildlife.

They can collect a sample of what they can including the painted black substance, which may have some use for Part 2 when seeking to dispel enchantments and protective wards on the island. The dockworker may also be used as a witness following the event, if witnesses are needed to apprehend the Acolytes or to collect more evidence.