It's always best to to add a notification to the page that the promo has ended. I'm a fan of the "did you miss out on this promo? Don't miss out on the next one! Signup now to stay in the loop" this way you keep getting emails that you can use for later. Make sure you add them to a new list specifically for this conversion. That way when you do go to email them they get a relevant email ... something like "You missed out last time, now's your chance!" or "We didn't forget about you ..."
As for altering the page - are you going to use it again in the future? If so just download the UB file for later use. Or, duplicate it. Rename the pages appropriately and change the URLs and unpublished the one you are not using.
Another option could be a redirect to a new LP where you have a new promo or are collecting email. It's really up to you. But, always make sure it is congruent with where they came from.
You could also use an overlay to notify visitors. When a new visitor lands a pop-up overlay is triggered that notifies them that the promo has ended. I would still collect an email here too. Then just grey out the buttons or disconnect them on on the LP.
Hope that helps.