Revealing mistake: When Ethan uses the magnetic screwdriver to undo the screws holding the grille to the air-vent in the NOC list room, the spindle that is actually turning the screw is visible after it falls out.
Revealing mistake: When we see a close-up of a knife being pulled out of a man's stomach, it's obviously a prop knife where the blade goes into the handle, as we can see the end of the blade while it's being pulled out. (01:19:50)
Answer: Krieger presumably used his knife to kill the rat in the vent. It's unlikely he would have tried to kill Ethan above the vault, as there would have been a noisy struggle which would set off the intrusion countermeasures. Luther would have also seen it happen on Ethan's head-mounted camera.
Sierra1
Also, Krieger didn't know how to communicate with Max.
Krieger didn't need to communicate with Max because he was actually working with Claire and Jim, and Jim was in communication with Max.
Krieger may have killed the rat with the knife, but that's not why it's in his hand when he confronts Ethan. After killing the rat, he has both hands on the cable holding Ethan.