Final answer:
The nurse should instruct the client to notify their healthcare provider if their stools appear tarry.
Step-by-step explanation:
When discharging a client at risk for venous thromboembolism (VTE) on low-molecular-weight heparin, the nurse should provide the instruction to notify their health care provider if their stools appear tarry. This is because tarry stools can indicate gastrointestinal bleeding, which is a potential side effect of heparin. Checking the aPTT every 2 weeks (option a) is not necessary since low-molecular-weight heparin does not require monitoring of aPTT levels. Massage of the injection site (option b) is not recommended as it can lead to bruising and tissue damage. Lastly, an IV catheter is not needed for administration of low-molecular-weight heparin (option d).