Sometimes minor carpet burns can be scraped out with a sharp knife by picking at it and raising the fibers at the same time.
If you have to cut out a piece of the carpet, follow any patterns so that the cut line will hide the joint. If you have to cut into a uniform carpet, try to follow any "grain" lines in the carpet. Put in the patch using double sided carpet tape under both the carpet and the patch. Be careful to cut and insert the patch following the same lie of the carpet, or else it will show up radically.