In January 2020, Parke sued Liberal MP Dave Sharma for defamation over a tweet in which he accused her of anti-semitism and "trafficking in conspiracy theories". She also sued Colin Rubenstein, executive director of the Australia/Israel and Jewish Affairs Council, and the West Australian and Herald Sun newspapers, over a press release from Rubenstein and stories run in the West Australian and Herald Sun that she alleged defamed her. On 8 January 2020 the West Australian published an apology and published an article by Parke. On 26 March 2020, the Herald Sun printed an apology to Parke and published her op-ed entitled "Criticism Not Same As Racism". In October 2020, the Federal Court dismissed Parke’s defamation action against Sharma, but 'was entitled to take up an earlier settlement offer from' David Sharma.