If I refinanced my mortgage in March 2020, is the balance as of Jan. 1, 2021, zero?

Yes.  The loans that were refinanced has a zero balance on 1/1/2021.  Just in case you have other issues use the information below.

If there is a refi and there was an outstanding mortgage principal listed in both of them on Line 2 on the 1098. When you do put an outstanding balance in both forms, then the program adds them together and if that number is greater than $750k, then it puts you in the category to "limit interest". To get that to go away, you need to go back to the deductions section and click on "edit" mortgage interest statement. Change the line 2 of the mortgage that you no longer owe on (like the one that you refinanced and paid off) to a 0 (zero) because you have refinanced out of that loan and no longer have an "outstanding mortgage principal". Once you change one of them to zero (the one that was paid off by the refinance) then it should no longer pop up with that error at the end when you go to file.