Filing Tax Return Electronically with an Underpayment Penalty Due

I just completed my mother's 2024 taxes and she owes the IRS money along with an underpayment penalty. She wants to file her taxes electronically, but send in the payment via regular check. How does this work with the underpayment penalty due?

 

The TT program asks when the tax payment will be paid and calculates the underpayment penalty based on the date I enter in the box. The penalty is $83 dollars if the payment is 'made' on 3/3/25 and increases to $99 if I change the date to 4/15/25.  

 

So if I file her taxes electronically tomorrow and we mail the check in for the payment, the IRS won't get the tax payment until a week or so later. Does this affect the amount of underpayment penalty due or will they 'honor' the underpayment penalty that is due and calculated at the time of filing her taxes electronically?

 

I can't find a clear answer anywhere. If they keep assessing an underpayment penalty until the day they receive the paper check, will they send her a bill for the difference? I haven't run into this situation before and hoping someone can clarify this for me. Thanks.