Some studies show that women should refrain from drinking green or oolong tea during pregnancy.
Here are the main cons:
1) Green tea contains substances that compete with folic acid. The latter is important for the development of fetus neural system.
2) Although less that coffee, green tea stil contains caffeine. Caffeine can increase the risk of miscarriage
3) As other sorts of teas, green tea makes it more difficult for body to absorb iron from food. This in turn can lead to anemia
As a bottom-line - avoid drinking green tea during the first trimester of the pregnancy. Don't drink tea together with meals. Don't drink more than 2 mugs of green tea per day.