It is not possible to remove the cigarette burn mark from your linoleum floor. Even though it cannot be fixed, you can replace the damaged area/section and replace it with a scrap piece from a less noticeable area like under the refrigerator or at the back of a closet. You may have to cut off the affected area and put a patch there as a replacement. It will be easier to conceal the patch if you have the same pattern. If, you have an extra piece trashed in your garage, nothing likes it. Otherwise, use a putty knife to scarp out the damages and the replacement piece. Try and remove as much adhesive residue as you can. Apply fresh adhesive on the back of the replacement piece and position it over the spoiled area carefully. You cab use bricks or any other heavy material to hold the patch down till the adhesive sets.
Burn it even worse with an iron, just say you got a shock from the iron(have ironed clothes handy and an iron with molten plastic on it) he can't shout at you if was an electrical fault