Does taking detox tea (bootea detox) affect my nexplanon birth control. The night tea has laxative the day time doesn't.?

No evidence. There is no evidence to suspect that this detox tea would impact the Nexplanon birth control. Of note there is also no scientific evidence that this detox tea would actually do what it claims or be useful. Save your money.
No. Please listen to Dr. Livingstone. If you get into the culture and mind-set of "detoxing", you may make yourself sick from drinking this weird stuff, and you will also never feel well again. Your body cleans itself, and the "scare" claims about technology filling the world with "poisons" are intended to make you feel unwell. It's a cruel scam. You'd do much better to join a fitness club.