Natalie,
Any platform output components can be deleted. If there is not an option specified under the red triangles to get rid of it, then a message can be sent to the platform's report output to delete the legend.
Here is a sample:
Names default to here(1);
dt=open("$SAMPLE_DATA\Semiconductor Capability.jmp");
ov=dt<<Overlay Plot( X( :PNP1 ), Y( :NPN1, :PNP2 ), Y Scale( Left, Right ) );
report(ov)[PictureBox(3)]<<delete;
To see the "Tree Structure" for the output, rt mouse click on the "Gray" triangle left of the red triangle, and select Edit==>Show Tree Structure.
There you will see all of the output objects for your graph.
Jim