It would probably damage the card.
But not the stamp. soaking has been the traditional way of getting stamps off of things since 1840. (If I remembered the date the first stamps were issued I could probably get the date within a week or so.
)
serious humidity might work too, like placing the card inside a compartmented container and a soaked sponge on the other side. Let it sit in the sun a while and see if the stamp comes off easily.
Steve B