Your mother's status with Social Security changed when she became a widow. The Medicare card reflects her claim's relationship with Social Security. For example, the card she had previously showed
that her relationship with Social Security was that she was entitled to benefits through her own work and had her Social Security number on the card with the proper letter designation to show that.
If she is now entitled to widow's benefits, the card will reflect your father's Social Security number and a different alpha code to reflect her relationship to your father. Based on the information you provided, Social Security and Medicare records are now set up to reflect your mother's new status. There does not appear to be an error that needs fixing.