It's not Joseph's parents, but I found some interesting possible records for Elizabeth Pritchard.
An Elizabeth Pritchard living with Tesseneers in the same area as a child:
"United States Census, 1860", database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MD6Q-6LK : 30 December 2015), Elizabeth Pritchard in entry for Nicholas Tessener, 1860.
Nicholas aged a bit fast, but this seems like it could be the same Elizabeth:
"United States Census, 1870," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MWDM-5TG : 17 October 2014), Elizabeth Tessonyear in household of Nic Tessonyear, North Carolina, United States; citing p. 1, family 5, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,658.
And then a marriage between a Joseph Tesseneer and an Elizabeth Tesseneer at the right time and place:
"North Carolina, County Marriages, 1762-1979 ," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:F839-DJB : 8 July 2016), Joseph Tessenyear and Elizabeth Tessenear, 16 Apr 1871; citing , Rutherford, North Carolina, United States, p. Page 11, Office of Archives and History, Division of Archives and Records. State Archive of North Carolina and various county Register of Deeds; FHL microfilm 428,312.