Step 1: A different way to check covalent character is through Pauling's electronegativity difference. Take Ca electronegativity as 1.00, and halogens as F = 3.98, Cl = 3.16, Br = 2.96, I = 2.66.
Step 2: The electronegativity difference for each bond is $\Delta\chi(Ca-F) = 2.98$, $\Delta\chi(Ca-Cl) = 2.16$, $\Delta\chi(Ca-Br) = 1.96$, $\Delta\chi(Ca-I) = 1.66$.
Step 3: A smaller electronegativity difference means less ionic character and more covalent character, since a purely covalent bond has $\Delta\chi = 0$.
Step 4: Since $\Delta\chi$ falls steadily from Ca-F to Ca-I, the covalent character rises in the same order.
\[CaF_2 \lt CaCl_2 \lt CaBr_2 \lt CaI_2\]
\[\boxed{\text{Option (C)}}\]