select the wire, and delete, or right-click the wire, and delete

Also, if you left-click select the net, you will see at least 2 green vertex dots and possibly one or more blue drag-to-add vertex dots (generally if a net has N green vertices, it will have N-1 blue drag-to-add vertex dots). If you double-left-click on a green vertex dot, it will be deleted. If you drag a blue dot it will turn green, forming a new vertex and two blue drag-to-add vertex dots will appear in the centres of the two new straight sections of the net that appear leading from the new vertex.