"How do I estimate what excess contributions $4430 plus earnings would be removed from some month in 2023?"
You don't; you can no longer remove the 2022 excess to correct it - this needed to be done by the due date of the 2022 return (April 15th or so in 2023).
The cheapest way to fix this would be to use up this carryover as a personal contribution (line 2, 8889) in 2024. TurboTax will try to do this, but if you did not restrain your 2024 contributions, you are likely to have another excess for 2024.
Because the 2024 excess (if one) was caused by the original 2022 excess, you will not be able to withdraw any of the 2022 excess (if the 2024 excess is larger, then you can withdraw the amount that is larger than the 2022 excess).
So, if you will be covered by an HDHP policy in 2025 with no conflicting coverage, the excess will carry over again to 2025 as a "personal" contribution. If you leave room for this contribution, then it will be "used up" in 2025, and the matter dealt with.
This would be much cheaper than the other way to deal with old excesses, so I user you to try to use up the carryover in 2024 or 2025. (Actually, TurboTax will try to use it up in 2024, depending on how much you contributed in 2024).
Please don't just remove random amounts from the HSA, because this amount is not only subject to tax but also to a 20% penalty.
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