I used to take intestinal cleansing products and did a ten day juice fast about 30 years ago. I used to take vitamin supplements. When I used to "cleanse" I did not worry about marijuana floating around my bloodstream and junking up the works or interfering with the process. But, nowadays i do not take vitamins, and do not cleanse.
Two years ago I found out about the Calorie Restriction Society and resveratrol, the stuff that's supposed to be good for you in red wine, which the human body produces naturally, but only when it's comsuming 30% less calories than normal. That was all I needed to know before I started dieting, and I lost 65 pounds in six months. No excercise, no cleansing, but I felt a lot better when i was done, and since then. I still am not "healthy" as i haven't started excercising on a regular basis, and still eat too much sugar and fat, but I haven't gained it back, and don't believe I will. (the reason I lost weight was because I was angry at the insurance industry, for denying add'l life policy...I showed them!)
I do believe in the body cleansing itself, but now i believe it does it on it's own schedule, not because i ingest something that I believe triggers it. Lots of water may help, but that's as far as I'd go these days.
I don't know about your cleansing process, but I do not believe that marijuana will effect it's outcome...and can only guess their answer, but maybe ask them...?
There is one cleansing process where people are made to believe they are flushing out their bile ducts, that doesn't work, they're actually creating bile colored stones overnight that they then pass (to make jewelry out of. hahaha)
I spent 20 years trying to figure out why i didn't/couldn't look good in shorts and a shirt...losing 70 pounds was the answer, but prolly only because I believe I look skinny to most people now.