Just add lty=NULL
plot.new()
legend("top",ncol=1,c("Mound reef (M)","Spur and Groove (SG)",
"Rubble Fields (RF)","Coral Walls (CW)",
"Mounds and rubble fields (MR)",
"Mounds, Monostand walls and Rubble (MMR)"),
pch=3:8, title="Reef Types",cex=1,lwd=2, lty=NULL)
EDIT
Removing lwd=2should be sufficient as Josh O'Brien pointed out, so your code should be:
plot.new()
legend("top",ncol=1,c("Mound reef (M)","Spur and Groove (SG)",
"Rubble Fields (RF)","Coral Walls (CW)",
"Mounds and rubble fields (MR)",
"Mounds, Monostand walls and Rubble (MMR)"),
pch=3:8, title="Reef Types",cex=1)

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