You're using our Landing Page feature to redirect web visitors who have completed a subscribe form (or another form), sending them to a personalized page upon form submission. Changes were made to that landing page in your account. The question is, do you need to do anything to update the subscribe form code?
Generally speaking, no. The Landing page is a hosted file in your account. Landing Pages are associated with a form via hyperlink and it is not hard coded into the subscribe form. Layout, images, colors and other design changes can be made to the hosted Landing Page in your account and will be reflected automatically.
If you were to create a brand new Landing Page to replace the existing LP in your existing subscribe form, changes would need to be made to the subscribe in your account (Assets > Forms) and the form code exported to reflect the change.