Your folks were assigned to Co. C, 3rd (Clack's) Tennessee.
No one by the surname Conder or spelling variant is listed in the Regiments Roll of Honor as having died during the war. See Lindsley's Military Annals of Tennessee.
Nor is a Condor listed in Gary W. Webster's "Confederate Roll of Honor, Known Confederate Dead Vicksburg Campaign, January 1862-July 1863, 1988" either in Vicksburg or the Confederate Dead Buried at Raymond, Mississippi."
Note, he may very well be buried in either place, however, full records of those buried were lost and only partial lists are available today.
You might want to contact the Old Court House Museum in Vicksburg to see if anything new has shown up.