I received a notification of repayment/refund data from my long-term disability insurance company. Does the taxable amount I returned in 2020 reduce my 2020 tax burden?

Repaid in 2020 goes into the 2020 return. See this from the IRS

https://www.irs.gov/publications/p525#en_US_2020_publink1000229600

Thank you, this was very useful!

Possibly.  What year or years did you pay the lump sum to the LTD insurer?  That year (or years), you are eligible for a repayment would create a Claim of Right issue.  The repayment credit or deduction would be reported on the current year's tax return.  Follow these steps:

• Down the left side of the screen, click on Federal.
• Across the top of the screen, click on Deductions & Credits.
• Scroll to the bottom of the screen for Other Deductions & Credits.
• Click on Other Deductible Expenses.
• Continue until you see the screen that states Repayments of $3,000 or less or Repayments of $3,000 or more depending upon your situation. 

For repayments of $3,000 or more, you also have the option of reporting a credit but you have to re-compute your taxes for the tax year that you paid the income.  See this TurboTax Help.