Final answer:
The client should remove the old twill ties after the new ties are in place.
Step-by-step explanation:
The correct statement by the client that indicates an understanding of the teaching is 'I should remove the old twill ties after the new ties are in place.'
When a client has a temporary tracheostomy, it is important to regularly change the twill ties that secure the tracheostomy tube in place. The ties should be removed, replaced with new ones, and the old ties discarded. This helps to prevent the build-up of bacteria and ensures that the tracheostomy site remains clean and free from infection.