According to the rules of war( 1907 Hague Convention of Land Warfare ) many of the "Greifkommando" soldiers were shot as spies/saboteuers. Many others died in combat when their cover blew of they engaged the enemy. Since they were wearing not the correct uniform and engaged the enemy wearing wrong uniforms they broke the hague convention which both parties were signatory to.

The same goes for using enemy equipment. Capturing vehicles from the enemy is common using those vehicles aswell but they have to get the markings of the army which is using them. During Greif US Vehicles were used with US markings and German vehicles got US markings.

Maybe somebody with better understanding of the law in question can answer to what extent it is relevant if and when the German soldiers might have switched to their German uniforms. Is it relevant how deep they passed into the American lines? If they had not passed the lines but lets say got wounded while approaching the front line and found wearing US uniforms?

Being POW requires you to be a lawful combatant, this includes wearing the uniform if you actively engage the enemy. There are certainly exceptions if the POW is not wearing and uniform while beeing surprised for example.