I received a lump sum pension distribution taxed at 20%. Part went to a Simple IRA. How will IRS know from my TurboTax return, what reduced this income for a tax refund?

The IRS will see two indications that you did a rollover.  First, after entering the Form 1099-R as TurboTaxToddL described, TurboTax will include the word ROLLOVER next to Form 1040 line 16 or Form 1040A line 12.  Second, the IRS will receive a Form 5498 from the SIMPLE IRA custodian showing the rollover contribution.

If you get a 1099-R that includes both a rollover (or money put back into the same account) and a partial distribution, just make sure that for the question "What Did You Do With The Money From (your retirement fund)?", answer "I moved the money to another retirement account (or returned it to the same retirement account)" (see screenshot) and that you did a combination of rollover and distribution. Enter the amount of the rollover here and it will not be taxable.

To enter your 1099- R in TurboTax Online or Desktop (you may need to upgrade to report these distributions), please follow these steps:

1. Once you are in your tax return, click on the “Federal Taxes” tab ("Personal" tab in TurboTax Home & Business)
2. Next click on “Wages and Income” ("Personal Income" in TurboTax Home & Business)
3. Next click on "jump to full list" or “I’ll choose what I work on” 
4. Scroll down the screen until to come to the section “Retirement Plans and Social Security”
5. Choose "show more", then IRA, 401(k),Pension Plans (1099-R) and follow the onscreen instructions

Please note that all distributions will be reported on your tax return (whether or not they are taxable) on Form 1040 on line 15(a) (or 16(a) but only the taxable portion will show on your return as taxable on line 15(b) (or 16(b)).