The old man is the Judo team's leader, he was fighting to get Shi(?(The guy that loves Taiga)) off the hook, and to allow them to get into the tournament thing for Judo. Judging by all the context I think that the "Envelope" you speak of was a picture possibly proving that the other kids provoked Taiga. Or if it was an envelope it was more than likely a confession, because earlier in the story we found out Taiga was told by the teachers not to say anything because then the school would be in trouble for neglecting bullying of Taiga.
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