How do I add Tax Exemption to an Existing Order Reservation or how do I remove the tax charge from an existing order?

There is no way to change the exemption on the order after is placed. You can not remove the tax.

In order to correct this situation, you would need to cancel/refund the order to credit "on account", which creates a positive balance in the customer's High Trek account. Then you would need to re-create the order with the exemption enabled on the customer and you would need to opt in for tax exemption when building the quote or in the Tax Section of the POS cart summary. Use the credit on account as the payment option.  Credit balances are stored under the customer's email address so make sure you connect the appropriate customer to the order that has an available balance.