Write the relevant electronic configurations

• $\mathrm{B}$ : $1s^2 2s^2 2p^1$
• $\mathrm{Al}$ : $[Ne]3s^2 3p^1$
• $\mathrm{Ga}$ : $[Ar]3d^{10}4s^2 4p^1$

Check Statement I

Statement I says: The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga.

Across group 13, first ionization enthalpy generally decreases down the group because atomic size increases.

So from $\mathrm{B}$ to $\mathrm{Al}$, ionization enthalpy decreases significantly.

But from $\mathrm{Al}$ to $\mathrm{Ga}$, the decrease is very small, and in fact the values are nearly the same due to poor shielding by the filled $3d$ electrons in Ga. This causes greater effective nuclear charge in Ga than expected.

Hence, the drop from $\mathrm{B}$ to $\mathrm{Al}$ is indeed much larger than that from $\mathrm{Al}$ to $\mathrm{Ga}$.

Therefore, Statement I is correct.

Check Statement II

Statement II says: The d orbitals in Ga are completely filled.

Gallium has configuration: $[Ar]3d^{10}4s^2 4p^1$

Thus its $3d$ subshell is completely filled.

Therefore, Statement II is correct.

Relation between the two statements

The filled $3d^{10}$ electrons in Ga shield poorly, so Ga experiences higher effective nuclear charge than expected. Because of this, its first ionization enthalpy does not decrease much relative to Al.

So Statement II supports the trend described in Statement I.

Correct option

Both statements are correct.

$\boxed{\text{Option C}}$