K.P.
Green tea as with any other tea is discouraged during pregnancy due to caffiene. The same can be said for breastfeeding.
Babies are often sensitive to caffeine intake of the mom (esp. if she avoided caffeine during pregnancy). This is particularly true of newborns to 6mo. as it is more difficult for them to digest/process it.
Sensitivity will result in a wide eyed, alert baby who doesn't sleep long and can be unusually fussy. It will take about a week to see a decrease in symptoms after a mom stops caffeine intake.
In short, it is up to you. You can try it but I would slowly introduce it. If your baby shows sensitivity then back off and try when he/she is older.
Also, just a footnote...there are many foods an infant can be sensitive to while breastfeeding like broccoli and other gas producing foods. If baby is particularly fussy, go back and take a look at what you've been eating. Chocolate cake is notorious for causing gas/loose watery stools.
I think it's wonderful that you are breastfeeding and the benefit your baby receives will far outweigh the temporary sacrifices you may need to make for a short time.
Best wishes for a wonderful experience and congratulations on your new baby.
K.
PS
If you decide to drink caffeinated items, just know that the levels will peak about one hour later, so try to time breastfeedings where they don't fall during that time period.