In a completely and adequately immunized child against Diphtheria, the throat swab was collected. It showed the presence of Corynaebacterium diphtheriae like organisms on Albert staining. These orgainisms can have one of the following properties on further laboratory processing -
This child is a carrier for C.diphtheriae.
Adequate vaccination can prevent the disease but not the colonization.

‘Mass immunization might result in disappearance of toxigenic strains from many populations but has no effect on carriage of nontoxigenic strains.’

Since the child is completely vaccinated, antitoxin level in serum can always neutralize the toxin but it can not prevent the colonization of nontoxigenic strain.
So, the organism can be grown on Potassium tellurite medium but since it might be a nontoxigenic strain, so any test to detect the toxigenicity will be negative.

Ref: Apurba Sastry’s Essentials of Medical Microbiology 1/e p246
It can grow on Potassium tellurite medium
It would show a positive Elek's gel precipitation test
It can be pathogenic to experimental guinea pigs
It can produce cytotoxicity in tissue cultures