Plot-wise, Justice Wargrave uses a strand of seaweed in order to create a distraction in Vera’s room so he can fake his own death. But the seaweed isn’t just a simple prop that will creep Vera out because it’s gross and slimy and stinky (or possibly delicious when wrapped around some rice and avocado, depending on the kind). Wargrave is specifically trying to scare Vera and bring about unwelcome memories:
And then, as she stood there, listening—a cold, clammy hand touched her throat—a wet hand, smelling of the sea… (13.67)
For Vera, the seaweed is a reminder that she allowed Cyril to drown and that the crime will follow her wherever she goes. And in the end, when Vera commits suicide, her last thought is of Cyril’s hand slash the seaweed:
Like an automaton Vera moved forward. This was the end—here where the cold wet hand (Cyril’s hand, of course) had touched her throat… (16.130)
The seaweed represents a past that Vera can never escape except through death—or, at least, that’s what Wargrave wants her to think.