You are correct that your spouse is not allowed to make any contributions in 2024. Those contributions should be removed as "return of excess contribution", or else they will be subject to income tax plus a 6% penalty.
Separately, you don't have excess contributions for 2023, so you can't use the special "removal of excess contribution" rules. If you got a check based on "return of excess contributions" and it is less than 60 days since you got the check, ask the HSA if you can re-deposit it as a rollover, or you might be able to open a second HSA at any bank that offers one, and deposit the same amount of money as a rollover. That way, it won't be taxed.
However, if that check was received more than 60 days ago, then you need to rely on @dmertz 's recommendation because he knows these rules better than anyone else on this board. If he says that is a "regular" distribution, then you either need to find some medical expenses to put against it, or else it will be taxed with a penalty.
