Troops will set traps and assist local hunters but won't use firearms. Over 100 people have been injured and at least 12 killed in attacks since April.
Justices were skeptical Monday that the case was an exception to other lawsuits against defense contractors, which usually get immunity in such litigation.
Twenty-three states have aligned with the Trump administration's stance that he has authority to bring in the Guard, while 22 back the district's position.