Do you think the following could be her? If so, you can send away for her Soc. Sec. info which would include parents' names for a fee.
Name: Mary Burdick
Birth Date: 21 Mar 1873
Birth Place: Phila, Pennsylvania
Claim Date: 28 Jan 1946
Type of Claim: Life Claim
Notes: 08 Oct 1976: Name listed as MARY BURDICK
Do not know if you got a copy of her marriage record to William Burdick but it might include parents names and/or a residence address which might lead to parents' names and would probably be cheaper than SS record.
Did you find Mary Burdick in the 1930 or 1940 census records?