The answer to 'carpet greasy' is that a greasy carpet is usually caused by a buildup of dirt, oil, and other contaminants. This can happen over time from normal foot traffic, spills, and the accumulation of skin oils and hair products. Symptoms include a sticky, shiny, or discolored appearance to the carpet.
The best solution is to have the carpet professionally cleaned. A professional cleaning technician will use specialized equipment and cleaning solutions to deeply clean and extract the grease and grime from the carpet fibers. This will restore the carpet's appearance and prevent further buildup. DIY carpet cleaning methods like spot cleaning or renting a steam cleaner may help, but are unlikely to fully remove the grease without the right tools and techniques.