Deception is never good? Uh... worked for Clinton, didn't it?
Anyway... deception is definitely the only way to go here, in my humble opinion. People who think you can just cheerily spout off to meddling parents about the cleanse... and have them NOT freak out are living in a parallel universe from the one I live in.
In MY universe... that is... NOT surrounded by a bunch of crystal-wearing, new age enlightenment types... people think the idea concept of not eating for weeks on end is not only scary and weird, but dangerous. I told TWO people and they call me incessantly to make sure I'm not DEAD. It's far easier to come up with some believable and harmless fib to deflect your parent's well-meaning but misplaced concerns.
I'd skip the entire dinner this week... feign sickness. It's rather gross but telling someone you're sick with really bad diarrhea usually works.