Which statement indicates a client understands newborn safety during induction of labor?

The statement indicating an understanding of newborn safety during the induction of labor is the one about checking the identification badge of anyone who removes the baby from the room. This practice is vital in ensuring the safety and security of the newborn in a hospital setting. It signifies that the parent is aware of the importance of verifying the identity of caregivers and hospital staff who handle their baby.

By checking identification, parents can prevent potential abductions and ensure that only authorized personnel are in charge of the infant's care. This precaution reflects a proactive approach to newborn security, which is a crucial aspect during the labor and delivery process.

In contrast, the other statements do not align with best practices for ensuring a newborn's safety. For example, sharing a photo of the baby in social media birth announcements may unintentionally expose the child to risks associated with online safety and privacy. Allowing a baby to sleep alone on a bed poses a risk of falling and suffocation, as it is not a safe sleep environment. Similarly, expecting nurses to carry the baby to the nursery without verification does not prioritize the checks necessary for the baby's safety, such as proper identification and security protocols in the hospital.