How to correct excess HSA contribution withdrawn as normal distribution

I have made a couple blunders specific to my HSA contribution/withdrawal and am trying to figure out how to clean this up correctly in my tax return. I would appreciate any feedback.

In 2023, I mistakenly contributed an excess $200 to my HSA account. I realized this while filing my taxes on Turbotax in 2024, and withdrew the $200 from my HSA before the April 15 filing deadline. My 2023 tax return did not report any excess contribution (i.e., in form 5329). However, I realize now that I did not withdraw the excess $200 through the correct process and instead withdrew it as a normal distribution. It shows up as a normal distribution on my 1099-SA for 2024 (dist code 1). I called my HSA custodian and they said it is too late and they will not be able to issue a new 1099-SA for 2024 and I should sort this out on my tax return in some other way.

How can I correctly account for this excess contribution that was withdrawn as a normal distribution? Is treating this withdrawal as "withdrawal was not used for qualifying medical expenses" the correct approach?