I have no issue with her deportation. But I wonder how US Immigration would have dealt with the Jew who survived WW2 by being a member of the SS?
That depends on how much you want to split hairs. What most people have in mind when they think of the SS (black uniforms with insignia that actually say “SS”, elite organization, centuries-long aryan pedigrees…) was the so-called Allgemeine SS (“General SS”.) Only the officers of the (para)military Waffen-SS were members of the former. Later in the war the Waffen-SS used some conscripts for the enlisted ranks. To make things more complicated, the units in charge of the concentration camps were part of the Allgemeine SS originally and part of the Waffen-SS later (although I’ve never heard of conscripts used in the camps.) The Allgemeine SS was mostly voluntary but e.g. when the police was placed under the command of the department of the SS, the higher ranking police officers were forced into the SS.
Btw. at this point that woman could only be tried for murder. For everything else commited before 1945 the statutory limitation periods expired long ago. Under current law there are several other crimes without time limits but that’s the result of later changes that don’t retroactively apply to people whose limitation period expired at some point.