So let me see if I understand what happened...
You received some medical services. The medical people would not bill your insurance, so you paid for the full amount of the bill from your HSA. You later submitted the bills to your insurance company. The HSA custodian sent you a 1099-SA for the full amount of the distribution. The insurance company paid you about $2k. You notified the HSA custodian that you want to report a Mistaken Distribution of $2k. You complete the custodian Mistaken Distribution form and send the custodian a check for $2k. The custodian eventually sends you an corrected 1099-SA, showing the HSA distribution to be $2k less.
If this is what happened, then you are OK. Yes, in case of a detailed audit, you will have $2k more in your HSA than your paperwork would suggest, but if you keep your paperwork as Critter suggests along with a note to yourself explaining how you came to this situation, I don't think that an amendment is necessary, since, as you already know, your tax would not change.
What concerns me is that you returned the $2k to the HSA custodian as a Mistaken Distribution, because if you just deposited the $2k without noting that it was a Mistaken Distribution, then the HSA custodian would count it as a personal contribution in 2019. This would give you an erroneous additional $2k deduction in 2019, possibly trigger an excess contribution situation, foul up the paperwork for the custodian, and, in general, create a mess.
While I hope that you did things the way I described it in the first paragraph, there is a better way to have done this:
1. Pay the medical bill out of after-tax checking account
2. When the insurance reimbursement comes in, deposit it to your after-tax checking account
3. Now that you know how much of the bill the insurance did not cover, ask the HSA custodian for a distribution to reimburse you for that amount.
Now, only one HSA distribution has been made, and it was for the right amount. No corrected 1099-SA, no extra paperwork, no possibility of accidentally depositing the insurance check as a new HSA contribution, no need to think about amending your return, and best of all, no reason to give the IRS a reason to wonder why you have more money in your HSA than the paperwork suggests should be there.
Hmmmn, most importantly, you should note that the HSA custodian does not have to honor your request to return a Mistaken Distribution. As the IRS instructions to the HSA custodian for the completion of the 1099-SA say, "As the trustee or custodian, you do not have to allow beneficiaries to return a mistaken distribution to the HSA" (see the TIP on page 1 at https://www.irs.gov/pub/irs-pdf/i1099sa.pdf). So for safety's sake, you want to avoid the need to report Mistaken Distributions as much as possible.