If you do not track your non-deductible basis on form 8606, then you will pay tax again when you withdraw the money. The IRS will not keep track for you. There is a penalty of $50 for not filing form 8606 when it is required, unless you can show reasonable cause. Form 8606 is one of those tax forms you should keep copies for your whole life, not just 3 or 6 years.
I would recommend filing amended returns to update the non-deductible basis in your wife's IRA. However, if you can calculate the basis yourself, and include a form 8606 with your 2023 return to add the new basis to the old basis, you can go forward from there, and only have to file the amended returns if the IRS questions your new basis.
