Once funds are in the HSA, they may be used for qualifying expenses for yourself, your spouse or your dependents, even if the funds were improperly contributed. (The rules and penalties for contributions and withdrawals are separate.)
You will pay a 6% penalty for each year the excess funds are in the HSA. The penalty is 6% of the excess contribution, or the balance of the account, whichever is lower. So if you can use the funds for medical expenses, and eventually spend down the money, the penalty will decline and eventually vanish. The other way to stop paying the penalty is to withdraw the funds, indicate they were not used for medical expenses, and you will pay income tax plus a 20% penalty.
So what you do depends on your medical expending, the amount of excess, and the amount of your account.
For example, suppose your balance is $5000, of which $3000 is excess, you spend about $2500 per year, and you don't plan on enrolling in an HDHP in the next two years. If you withdraw the excess and don't use for medical expenses, you will pay over $1200 in tax and penalties. If you just spend the account for medical needs, your penalty this year would be $150 and next year would be zero because the account would be empty.
On the other hand, suppose your balance is $20,000, your excess is $3000, and your medical needs are $1000 per year. You will pay about $1200 in income tax and penalties if you withdraw the money and don't use it for expenses, against $180 per year for the next 20 years.
