Haven't got the slightest idea what that detox program is, so can't advise you, but in general, what you eat or don't eat should not effect this medication.
http://www.webmd.com/diet/features/lose-21-pounds-in-21-days-the-marthas-vineyard-diet-detox
and mvdietdetox.com if you where interested in looking into it. Thanks for your time.