An appointee of President George H.W. Bush, Souter spent more than 19 years on the Supreme Court.
The decision leaves Holmes with the Supreme Court as her last chance to undo her conviction. She will have to ask the court to hear the case.
How a Supreme Court decision paved the way for more punitive policies
The court's decision split its nine-member bench along ideological lines, with its three left-leaning judges opposing.
Nicola Sturgeon has warned that trans lives could become 'unliveable' following the Supreme Court judgment on the definition of a woman.
Paapa Essiedu signed a letter standing 'in solidarity' with members of the LGBT + community 'impacted' by the Supreme Court gender ruling.
The administration claims judges are interfering with its power over immigration and foreign policy.
Transgender women have been blocked from taking part in all levels of women's cricket, the England and Wales Cricket Board has declared.
The decision comes in response to the Supreme Court's ruling last month that the term 'woman' in equality law refers to a 'biological woman'.
The British actress, 35, as been among those speaking out in the past in opposition to the Harry Potter writer Rowling's opinions on gender.