It depends on when this happened.
First of all, you are correct that, although each person's eligibility is determined separately, they are linked.
Second, if you remove your 2023 contributions by the tax deadline (April 15, 2024), then it is as if you never made them. That could allow your spouse to contribute more, depending on the type of insurance each of you have. For example, if you are both covered by a family HDHP, your overall limit is $7750 jointly, plus $1000 individual catch-up contribution. Suppose you contributed $6000, your spouse would be allowed to contribute up to $3750. Then, suppose you were only eligible for 3 months in 2023, which makes your limit $1937 (from the family limit) plus $250 (from your catch-up) = $2187. If you remove the excess of $3813 before April 15, 2024, it will be as if you never made that contribution. That would make your wife's contribution limit $5813 ($7750 family max minus $1937) plus her $1000 catch-up, equals $6813.
Of course, this assumes your spouse is covered by a family HDHP for the entire year and has no disqualifying coverage. If she is covered by a single HDHP, or if you switched from a family HDHP to a single HFHP when you went on Medicare, her limit will be calculated differently.
If the excess was contributed in 2022, you need to pay a penalty on that, or remove it and pay income tax. What you do now will not change your spouse's 2023 limit, and it is too late to make a corrective adjustment to 2022 that would allow your spouse to contribute something retroactively.
