How do I make a button disappear after certain amount of minutes?



I want to add some scarcity to my Unbounce landing page. My idea is to make a button (with its underlying link) disappear after say 60 minutes.

I will be inserting some external code from a countdown timer so the user can see actual countdown and feel the scarcity. However, I also want to be honest and make the offer (the link button) actually disappear after those 60 minutes.

Any idea on how I can achieve this?