Your contribution limit for 2019 is not affected by an insurance change in 2020 unless you relied on the last month rule.
The last month rule says that, if you were eligible for an HSA on 12/1/2019, you can contribute the full amount for 2019 even if you were not eligible earlier in 2019, but only if you also maintain your eligibility for all of 2020. If you used the last month rule, and lost your eligibility, your 2019 contributions become retroactively disallowed and you will pay a penalty on your 2020 tax return. If you were eligible for all of 2019, your insurance change in 2020 does not change that.
For your 2020 contributions, you need to request a "return of excess contributions" from the HSA bank. This is a special form, not a normal withdrawal. The excess amount is not eligible for a tax deduction so it will be included in your 2020 taxable income. If you don't have enough left in the account to remove the entire amount, remove as much as you can. You will pay income tax on the entire amount as part of your wages (the deduction is not allowed) but the penalty is, I think, 6% of the excess contribution or 6% of the remaining balance whichever is less, so remove as much as you can if you can't remove the entire 2020 contribution. Any earnings on the 2020 contribution must also be withdrawn and that will be taxable interest on your 2020 tax return (you will get a 1099-INT).
