This is a good question. There are two main reasons.
First, we want to publicize what Peter Singer and others have called “effective altruism”—that is, the practice of giving money away in such a way as to maximize its positive effects. We hope that by publicizing this giving process, we maximize the chances that someone else who is going to give money away will do so in a manner that is also calculated to provide the most help for the most people. We further hope that someone who might not otherwise have given money away will be inspired to do so.
Second, we want to spread the word about our law firm. Of course, we have self-interested reasons for doing that—it’s good marketing (although if our only goal was marketing, we could think of more efficient ways to spend $100,000). But spreading the word about our firm will help others in the long run because this will not be the last time that BT gives away a significant chunk of money. By bringing more cases to our law firm, we increase the amount of money that we’ll be able to give next time.