MR. BMJ, as you already know, I was the one who had mentioned that a study showed a reduction in testosterone with green tea extract, but from further readings, this may not be the case. I found the full text of the original study and they INJECTED the catechins in mice and showed dramatic reductions in appetite and hormone levels, with ECGC being the most potent. But when given the extract or individual catechins, there was no significant effect, most likely due to the poor absorption or rapid metabolism of the catechins.
Another study looked at the availability of catechins from green tea and found the same thing, low bioavailability. From this evidence I don't think that green tea is going to affect hormone levels to any extent, and the studies on green tea extract show some impressive effects of the its components.
As for the best time to use green tea, I would suggest using it with every meal, as studies have shown it to reduce carbohydrate digestion and absorption, along with a thermogenic effect, due to MAO inhibition and caffeine.