Love the idea. I hope it raises a ton of money.
I once went to an event where the favors were indeed tea bags, but they were tucked into little felt teapots -- just find or draw a very simple outline template of a teapot shape, maybe 4 inches across, on colorful felt; cut two shapes out and use fabric glue or tacky craft glue to glue the edges and spout to each other but leave an opening in the "top" of the teapot big enough so you can slip in a few teabags. If you like, use fabric paint pens to decorate one side of the felt teapot with a simple flower design, or whatever you like, or the words "Thank you."
If that's too fussy, make a paper teapot with two sides instead and slip the bags into that. The felt looks really nice but if you don't want to spend that much, try nice, heavy craft paper. There are papers with "teatime" sorts of designs on them, too.