The role of a catalyst is to change:

A catalyst provides an alternate path for the reaction without changing the initial and final state of the reaction energy profile.

Hence, the use or presence of a catalyst won’t bring any change to state functions, i.e., the functions that are only dependent on the initial and the final state.

We know that the Gibbs free energy, Enthalpy and Equilibrium constants are all state functions.

Hence, a catalyst can not change or alter any of these and we can conveniently rule out options A, B and D.

The path provided by the catalyst though is in such a way that the activation energy, i.e the energy required by the molecules to convert into products, either increases or decreases. 

Based on this change in activation energy, the catalyst is either +ve or -ve

Hence, the correct answer is C: activation energy of reaction