I saw a clip of this and gotta say they make way too much drama around this. Have security remove it casually like any other item thrown on the court. Throwing a towel over it to hide it and generally turning it into a bigger deal than it is will just motivate people to do it more.
At this point, with all the cameras it's easy to find the thrower and kick them out. The key is to make sure the stunt isn't worth it for them. This is coming from a non-american though so there's less ingrained prudeness I guess. If someone would throw a gun on a European court we'd be similarly shocked.