What you need to do is this:
1. Contact your insurance company and ask them to send the money to you, not your HSA administrator.
2. Contact your HSA administrator and tell them that you had a "Mistaken Distribution" (i.e., money paid out of your HSA that it turns out was not for a qualified medical expenses). Why was it not qualified? Because the expense should have been reimbursed by insurance - expenses to be reimbursed by insurance are not qualified medical expenses for an HSA.
3. If the HSA administrator accepts your request, then they will have you sign a form about the mistaken distribution, and then you will send them a check for that amount. This is why you need to do step #1.
The HSA administrator should also issue a corrected 1099-SA documenting your HSA distributions for the year (i.e., making sure that this mistaken distribution is not included in the 1099-SA for tax year 2020).
In no case should this "refund" be considered a contribution for either tax year, that's not the right treatment.
Instead, doing it this way makes the HSA administrator set your account correctly in case of audit. In any case, make sure that the HSA administrator treats this amount of money as a mistaken distribution and NOT as a contribution.
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