Final answer:
A PCT should document and report coffee ground emesis to the nurse immediately due to its significance as an indicator of potential gastrointestinal bleeding and the need for urgent medical attention. Maintaining hygiene is also important but secondary to reporting.
Step-by-step explanation:
When a Patient Care Technician (PCT) observes coffee ground emesis in a patient, it suggests the presence of old blood in the vomit, which is a significant clinical finding. The appropriate action for the PCT is to document the finding and report it to the nurse immediately since it may indicate a serious underlying condition such as gastrointestinal bleeding. While maintaining patient hygiene by cleaning the patient and changing bed linens is a component of care, this does not take precedence over reporting critical clinical findings. Offering the patient water may not be appropriate without the nurse's guidance, as the patient may require specific medical intervention. Ignoring the finding is not an option as it is clinically significant and needs urgent medical attention.