We check each combination one by one.

A. Chlorophyll - $Co$

• In chlorophyll, the central metal ion is magnesium, not cobalt.
• Chlorophyll contains a porphyrin-like ring with $Mg^{2+}$ at the center.
• So, A is mismatched.

B. Water hardness - $EDTA$

• Hardness of water is due to $Ca^{2+}$ and $Mg^{2+}$ ions.
• $EDTA$ is used in complexometric titration to estimate hardness because it forms stable chelates with these metal ions.
• So, B is correctly matched.

C. Photography - $\left[Ag(CN)_2\right]^-$

• In photography, the fixing agent is hypo, i.e. sodium thiosulfate, which dissolves unreacted $AgBr$ by forming the complex: $[Ag(S_2O_3)_2]^{3-}$
• The complex $\left[Ag(CN)_2\right]^-$ is associated with silver cyanide chemistry/electroplating, not photography.
• So, C is mismatched.

D. Wilkinson catalyst - $\left[(Ph_3P)_3RhCl\right]$

• Wilkinson catalyst is indeed: $\left[(Ph_3P)_3RhCl\right]$
• So, D is correctly matched.

E. Chelating ligand - D-Penicillamine

• D-Penicillamine can act as a chelating ligand because it has donor atoms capable of binding through more than one site.
• It is also used medicinally as a chelating agent for metals like copper.
• So, E is correctly matched.

Therefore, the mismatched combinations are: $A \text{ and } C$

From the given options, this corresponds to: Option C.