I'd make a locked and/or invisible field (or maybe a slider) somewhere to track the number of moves the player has remaining.
If you're displaying search results as a bunch of links in a field, you could make clicking a link count down the remaining moves by overriding the "link" event for the field. The default handler for link events is
on link x do go[x] end
So you could instead give the field something like
on link x do moves.text:moves.text-1 if moves.text=0 go[theGameOverCard] else go[x] end end
Side note: you can also write that conditional as:
go[if moves.text=0 theGameOverCard else x end]
This approach might be a little weird, though, since it ignores the user's final selection and surprises them with a game over.
If the cards you can get to via search have a "back" button, maybe it would make sense to test for game overs there, and navigate to the final card instead of the search page?