You were supposed to enter the second stimulus payment in your 2020 tax return, even though you received it in January 2021. So it appears that you claimed a credit that you were not entitled to, and the IRS letter is correct. You probably have to pay the amount that they say you owe.
But eliminating a $1,200 credit should not make a difference of $2,000. On the Form 1040 that you filed, is the amount on line 30 $1,200, or is it more than that? Does the letter say that anything else was wrong, or that they changed anything else? They are probably adding penalties and interest. The details should be in the letter. But I would not expect the penalties and interest to amount to $800.
