We got married in feb 2020. My wife was was a MD resident till june, and then she moved with me to MO. Why is she paying an extra non resident tax of MD ?

Your spouse was a Part-Year resident of Maryland.  She would report and pay tax to Maryland for any income she earned in Maryland- check the Maryland return to make sure she only reported Maryland income.

.For Missouri, a part-year resident is treated as a nonresident but may determine tax as if a resident for the entire year.

As a part-year resident, you may take either the Missouri resident credit or the Missouri income percentage, whichever is to your benefit. On a joint return, one spouse may take the Missouri income percentage and the other the Missouri resident credit.