In their letter, her lawyers said: "As we are sure that you will readily understand, being subject to a police investigation is highly distressing for any person, but especially so for a teenager, particularly one who has been recently subject to such adverse media coverage.
"In such circumstances, we believe that the police must weigh carefully the extent to which an investigation relating solely to social media activity is merited."
Paris's lawyers said it was "immediately apparent" from reviewing the Twitter material that it would be "inconceivable" that they would form sufficient grounds for a prosecution.
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The group arrived at the harbour early on Tuesday morning on what is thought to be a fishing trawler stolen from France.
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