Anything alkaline will break up head grease, keep in range of 9-11 but remember higher pH the more need to neutralise.
With greasy soils it's also about the temperature, greasy substances are more mobile and free rinsiong the higher temperature they get. Think about when you fry sausages or something - if you pour the fat away straight after cooking, no problem, however if you leave it all to go cold in the pan and then tried to rinse it out with cold water you'd be there all night.
Higher rinse temperature will give quicker and better results. On severe build-ups you can only get it out so much at a time, there is no wonder product that'll make it all vanish in one go I don't think! Several "normal" wet passes with the wand/hand tool will give a better result and be kinder to the carpet/fabric. Also use your HWE in combination with a nappy towel, tampico brush or even better a Minitex. Spray, agitate, dwell, rinse, spray, agitate etc etc....
