Final answer:
The last piece of PPE a phlebotomy technician should remove after exiting a patient's room are the gloves. This is to prevent the spread of contamination and follow safety protocols.
Step-by-step explanation:
After exiting a patient's room, a phlebotomy technician should remove gloves as the last piece of personal protective equipment (PPE). The proper order for removing PPE is to first remove the gown, then protective eyewear or goggles, following that the mask, and finally gloves because they are most likely to be contaminated. It is crucial to follow this order to prevent the spread of infection and ensure the safety of the technician and others.