Just go down to the texture list and click the red icon with a white X on the texture you want to remove. The icon with a green arrow replaces the texture with one selected in the asset browser. The magnify glass selects the material in the asset browser. What the binoculars does I have no idea.
If you only have 1 texture you can't remove it, simply add another texture and choose the Paint Material tool under Modification Tool; and simply paint the new material where you don't want the old one.