If any part of your DW is still greasy after a full cycle you are not using enough detergent, hot enough water or the correct cycle for what you are washing. I see this all the time when repairing DWs here, often when I remove the sump cover from a GE or WP built Tall Tub DW the bottom is covered in greasy gunk. Then I go to the next house and work on the same model machine and there is no greasy gunk at all. I believe that part of this is caused by only putting detergent in the one main wash cup and or using detergent tablets again only in the main cup. I always suggest to my customers that if using the detergent tablets to also use some regular detergent in the first wash cut. And for the DWs that don't have a first cup I suggest putting at least one table spoon of detergent on the door before starting the machine.

Proper dishwasher performance is a very fine line between the proper amount of detergent, water condition and temperature amount of food soil and the cycle used. There are no hard and fast rules for all dishwashing situations. But if you notice grease left behind something is not ideal, the greasy buildup can destroy plastic and rubber parts of the machine and cause clogging problems in the DW and in the household drains.

Yeah, I've got to chime in that the filter on my Miele (Premiere Plus) STAYS greasy, despite 150F washes and Miele tabs. I've run Finish dishwasher cleaner through it, and that seemed to mollify the grease (at 170F), but a few standard washes later it's back to schmutz.  Before anyone asks or accuses; yes, I scrape thoroughly, and no, I don't pre- rinse.  (disclaimer) It is, however, my common practice to use only 1/2 Miele tab.  Dishes, unlike filter, are sparkling.   I even tried adding a level tsp of TSPP to the detergent dispenser, to little effect. I used to think it was the rinse agent, but now, I just don't think about it.