Scratches cannot be ground out at an opticians. If your lenses are coated it may be possible to strip the coating off and this might get rid of the scratches.
(Providing that the scratch hasn't gone straight through to the lens material)
If it's just a single vision lens, then depending on your prescription they may be able to put a new lens in for you on same day, which won't cost all that much.
A hard coated lens does help reduce scratches but does not make them indestructable.