The English-speaking world seem to insist on pronouncing it Pill-art-ease. There seems to be no logical reason for this. The guy that invented it, Joseph Pilates was a German, but moved to the states. Even when he lived in the states he never ever pronouced his name as Pill-art-ease.
The correct pronunciation is therefore pi-lart-es if it were spoken in German, but a slightly anglocised version would then be puh-lart-es. But in no way would it be pill-art-ease.
Interestingly enough if you point this out to most English speakers, including pilates instructors they will continue to use the incorrect pronunciation. I'm guessing it is because they are afraid that everyone else will think they are mispronouncing it.
Most dictionaries I've seen also show it with the incorrect pronunciation.
ANyway - that's the trivia for the day