Please, read this BBC News article about the court case: LinkedIn told it cannot stop the bots.
Many things LinkedIn users do are against LinkedIn User Agreement and / or LinkedIn Professional Community Policies, including creating a false identity, connecting to people you do not know, managing multiple LinkedIn accounts on someone else's behalf, etc. Please, read LinkedIn | User Agreement:
But Linked Helper does not hack LinkedIn, it can do only those things, which you can do manually!
So it seems, that it’s legal to use Linked Helper, but it’s against LinkedIn rules.