Excess contributions for 2020 can be corrected by obtaining a return of excess contribution. The HSA custodian will calculate the investment gain or loss attributable to the contribution being returned and distribute the adjusted amount to effect the return of the amount of contribution requested to be returned. Any attributable gains distributed will be taxable as ordinary income on the tax return for the year in which this distribution is made.
The excess contributions for years prior to 2020 can only be resolved by making regular, taxable distributions of the excess amounts. Regular taxable distributions (those not reported as used for qualified medical expenses) are also subject to an early-distribution penalty (additional tax) of 20% if the distribution is made before you have reached age 65. This makes the excess contributions you made for years prior to 2020 extremely expensive since they will not have been excludible from income on the tax returns for the year for which the contributions were made, are subject to 6% excess contribution penalties each year that they were in the account (including the year for which the excess contribution was made), the money taxable again when the excess is corrected by a regular taxable distribution and potentially subject to the 20% additional tax. For example, if you are under age 65 (which seems likely since you had a child in 2015) and made an excess contribution of $3,350 for 2015, that excess contribution will have accumulated 30% in excess contribution penalties, and the corrective distribution in 2020 will be subject to a 20% additional tax and ordinary income tax. If your marginal tax rate is 22%, that means that 72% of that contribution will be lost to income taxes and penalties and will also have not reduced your 2015 taxable income. Excess contributions for later years will have accumulated a smaller percentage in excess contribution penalties but will still incur the same income tax and 20% additional tax upon correction. (I'm assuming that the year-end balance in your HSA each year was greater than the sum of your excess contributions; the excess contribution penalties are 6% of the lesser of the amount of excess contributions or the year-end balance.)
The only other thing you could potentially do is spend the HSA down to zero on qualified medical expenses before the end of the year. With a zero balance in your HSA you would have no 20% penalty but you would still retain the excess contribution total to come back to bite you if you ever made another HSA contribution that brought your year-end balance above zero.
