Have you ever accidentally burnt your rug, let's say by leaving straighteners on it or maybe ironing on the floor? Burn marks can be really tricky to get our of carpets without it leaving a noticeable trace. If the mark is only on the surface of the carpet you maybe able to scrub it out with steel wool or a lightweight sandpaper, this should get out any small marks, after this you will need to vacuum the area to get rid of any wool fibres or residue sandpaper.
Although this method is a sure fire way of getting rid of small surface marks, it may not work on much deeper piled carpets where there is a much visible mark still left after rubbing it with steel wool. If this is the case for you then you will have to use a utility knife to cut around the area, try to make the cut out a square of rectangle. This patch will then have to be filled by another piece of your carpet, this could be a remnant that you kept after the carpet was fitted, if you have not kept this then use a piece that is not seen regularly like underneath a sideboard or chest of drawers etc.
Use the cut out piece of carpet as a template by drawing around it onto a piece of paper, then choose somewhere to cut out your new piece of carpet. Using a glue gun, glue the underside of the new patch and fit it into place. Glue around the edges to make sure the piece will not become dislodged when cleaning. Use a carpet tractor to roll the carpet piece into place and make sure the pile is nicely