Media lawyer Paul Gilbert has told Daybreak that judges will have to decide on "whether or not a tweet itself is more than shocking or offensive."
He added: "It's finding a balance between what the law says about this and the freedom of speech."
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Armed police have carried out a raid apparently linked to Wednesday's deadly terror attack in Westminster.
Cheryl Grimmer vanished from inside a beach shower block in Wollongong, Australia, in 1970, when she was just three.
Pc Keith Palmer was on the front line and because of his actions, the Westminster attacker was unable to kill anyone else.