Focusing strictly on if Chase claws back credits or not, in the past they have been very lax about it or I might even say, clawbacks with Chase were close to non existent. I'm talking about if someone purchased an item, or booked an airline ticket/hotel, and then received a credit (from an offer or card benefit) or points bonus for those purchases and then they returned or canceled the purchase, Chase would not take back the credit or the points. So this was free money/points in the cardholder's pocket. I've personally not done this but have read many DPs of this being the case. As of a few months ago, Chase did begin to claw back The Edit credits for those who canceled their hotel booking thus disappointing many who were looking to make an easy $250 - Chase wasn't making any money from their hotel booking so they weren't going to just let the cardholder make money off of them. Besides for the point that the credit was actually meant to be used for an Edit hotel booking and if you no longer have one then you're not entitled to the credit. If you make a new booking they'll give it to you again, no problem.

However, in the case of the OP, they are NOT canceling their booking, they are just canceling the card. So Chase still has whatever they paid for the booking and therefore I don't see why they would not allow them to keep the $250 credit used against that. When you paid your previous AF you were paying to get all the benefits for the following 12 months including any new ones that would be added during that time period. So you're fully in your right to use this $250 until your next AF which resets your rights to benefits for the following year - if you renew you get them again, but if you don't you shouldn't lose what you had the right to from the previous year's AF. Benefits that are provided for a calendar year (vs cardmember year) are the same - you should get them until your next AF is due. It works this way with Amex too and they are sticklers for clawing back anything that they feel doesn't belong to you but they won't claw back credits that you legitimately got while you were still a cardholder (as an example, if you apply now for a Platinum card, there are benefits that you will be able to use in 2025, 2026 and in early 2027 until your next AF will be due and you can then cancel without fear that Amex will take any of that back).

Also, the Chase terms stated if the credit was received within the last 90 days it may be reversed, so for example I make a booking today for next July and get the $250 credit, but then I cancel my card some time in May, it's long past 90 days from today so there would be no clawback. I don't see why someone that cancels in January or February would be subject to that clawback either; they aren't doing anything differently except canceling a bit earlier because they don't want to pay the increased AF.