It's a confusing topic. The Vitamin E study in 2011 that is often cited in articles was considerably flawed because they only used the α-tocopheryl component of vitamin E. Good vitamin E supplements are broad spectrum and include all eight forms of Vitamin E - four tocopherols (alpha, beta, gamma, delta) and four tocotrienols (alpha, beta, gamma, delta).
You have to be careful with supplements. Many are a waste of money. Some may even be bad for you. I tried Ginko Biloba many yrs ago on a whim and it gave me severe bruising. No more whims for me - just research! Some high-grade supplements can be very helpful depending on your situation. I've use very good liver detox supplements myself since I've had so many chemo episodes my liver markers are usually elevated.
It's probably true that anti-oxidants in general are probably a bad idea to take during chemo since they might interfere with the metabolism processes going on. You have to sift thru the research.