Generally, when we think of interest group influence, we think of the legislative branch. Even the term "lobbyist" comes from those hanging out in the lobby of Congress to speak to its members. But interest groups can also lobby, or try to influence, the other two branches or the bureaucracy. Here is a good example of how interest groups can effect public policy through the judicial branch.
In the 1950s, Congress passed a law saying that if a religious group endorses a political candidate, they could lose their non-profit status. There are some who think this violates the free exercise clause and the principle of separation of church and state, and want to challenge the law. Therefore, on Sept. 28, a bunch of pastors will give political sermon, in defiance of the law, and the IRS has been informed that this will take place.
This is not as unusual as you might think. In the US, the courts cannot simply look at a law and declare it unconstitutional. They must have an actual case before them. This is not true for all democracies. So, if an interest group wants to challenge a law, and there are no current cases suitable for this purpose, they might create a case themselves. I can think of two other recent examples when this happened and went to the Supreme Court: the DC gun law case, and the Texas sodomy law case.
Ban on Political Endorsements by Pastors Targeted - washingtonpost.com
Update: NPR also ran a piece on the story.