Grease stains are almost impossible to remove from surfaces, including carpets and table. While the first line of precaution would be to keep your home accessories and your carpets save from any such stains, there isn't a lot that can be done in this regard in the case of an incident. When the deed has been committed, there is no need for ruing the carpet, but you should instead get to work.
What you need to do is to create a mixture of alcohol and salt. There should be four parts of alcohol for every one part of salt, so follow the measurement while making the mixture. Once the mixture is created, rub it on the stain and vacuum away the particles of salt once the stain has been removed. This method almost always works for us.