If Medicare is effective February 1, that is the date you must use, even if it was not “primary“. Your maximum allowable contribution for 2021 is $600. Everything over that must be withdrawn and it will be added back to your taxable income. That’s why it is increasing your tax, because you don’t get that income tax free any longer. However, you won’t pay a penalty if you withdraw the excess contributions in time.
However, you seem to be unaware that if your wife is covered by a qualifying HDHP and does not have other insurance, she can also contribute to an HSA in her name, even if she is not the primary person named on the medical insurance policy. She can open an HSA at any bank that offers them; my local credit union offers an HSA with a service fee of $3 per month. You may be able to find HSAs at many banks either local or online.
Your combined maximum is also $7200 for the year, so if you are limited to $600, your wife could contribute up to $6600 and take a tax deduction for that amount. She can make contributions for tax year 2021 up through April 18, 2022, as long as she notifies the HSA bank before she makes the contribution that it is for the previous year. Since you must withdraw $2908 from your HSA, that amount could be contributed to your wife‘s HSA and zero out the tax that you would have owed on the excess contribution. Or, you could contribute more, up to $6600. If your wife is still covered by an HDHP, she can make contributions in 2022 as well.
