Hate to dissapoint you, but I'm pretty sure that they've given out either green T-shirts or green rally towels at every home playoff game this year.
The towels all advertise the Mass State Lottery. Really cheap, crummy quality. The shirts have all displayed the Celtics' alternate logo (white disk with green shamrock) on the front. At the first game, the shirts had "Reebok" in big letters on the back, and they were Reebok-brand shirts (on the label). Other shirts have been from a variety of manufacturers, with fairly small advertising on the front. So far, I've seen Reebok, Arbella, TicketMaster, and the Lottery. Quality of the shirts has varied widely; I think I have four so far ... not sure. I haven't seen "Adidas" but I would not be surprised if there are Adidas ads on some shirts.
The towels, in my opinion, are kind of stupid, but I've been glad to have them. The paper towels in the mens' rooms run out in the second half! As for the green shirts, a few years ago Pierce said how much he likes to see a sea of green out there, so I always wear green to the playoffs. I have white, tan, grey, black, and green Celtics gear, but for the playoffs I stick to a green shirt. Not because anybody told me to, not because they gave me free shirt, not because of the advertising, and I don't have a pink hat.
I wear green to proudly display my team's color, and to do my part to support the team. If Pierce likes it, it's OK with me. He said that all the green was the reason why he called the Garden "The Jungle." If anyone else wants to wear green, I think it's great. If they wear something else, that's cool, too. I can't see criticizing anyone for wearing green to the game.