If I transfer $25,000 from my matured IRA into my savings account, will I have to pay the 20% withholding to the bank?

Yes, if the bank is the IRA custodian.

Withholding is an amount taken out of payments of taxable income to you in anticipation of your tax liability. It is no different from the amounts withheld from your paycheck. If you are not retired and are taking an early distribution from your IRA, the administrator of that IRA is required to withhold 20%, which is then paid to the IRS. When you prepare your tax return for the year, this amount is included in your taxes paid to help determine whether you get a refund or not.

It is not paid to the bank, it is withheld from your distribution.

Also keep in mind that (a) if you are under age 59-1/2 in addition to regular federal income that you owe on the distribution you would also owe an additional 10% penalty for taking an early withdrawal, and (b) you may also owe state/local income tax on it, depending on where you live.

Scott and ebaines both make good points.

Why are you withdrawing the money?