If the giver chooses to pay the fee, the fee is added to their total donation amount, so that when the fee is deducted, the church receives their full intended donation.
If the giver chooses not the pay the fee, nothing is added, so when the fee is deducted, the fee is essentially being covered by the church.
So, either the giver covers the fee, or the church does.
In both cases, the fees are deducted before being deposited into your church bank account.
You should always record the donation amount that the giver chose to give - the entire amount (including the fee, if they chose to cover it) is tax-deductible.