Take-off tires, in racing, are used race tires pulled off a car with usable life left and resold cheap. In the consumer tire market the same phrase means near-new tires with under 50 miles on them.
Search “take-off tires” and almost everything you find is about street tires: Champtires, a used-tire retailer, defines them as “tires that have been driven on for less than 50 miles” — near-new, the opposite of worn. In a race pit the word runs the other direction. Take-offs are somebody else’s spent-but-not-dead race tires, often a better-funded team’s, sold off the trailer or in a Facebook group. What you are buying is remaining tread and remaining heat cycles, and the second one is invisible. Measure the tread, put a durometer on it, and ask how many nights it ran and on what surface. If the seller cannot tell you, price it as scrap and be pleasantly surprised.
Take-offs are the cheapest speed in grassroots racing when you know what you are buying, and an expensive night when you do not.