If you don't support LinkedIn and have blacklisted or firewalled them: good. That's the correct professional response to any abuser/attacker.
If you haven't blacklisted/firewalled them, then you'll want this:
Remember to block all IP traffic bidirectionally so that LinkedIn can't reach your network and so that anyone on your network can't reach them. This is especially important if you run mailing lists, since LinkedIn will spam those too. I also recommend checking to see any of the spammers who work for LinkedIn have managed to get on your mailing lists: if so, unsubscribe and ban them.