lagrangian formalism - Boundary terms and Symmetries

Consider Maxwell-Chern-Simons theory in 2+1 dimension, with Lagrangian

$$L = -(1/4)F_{\mu v}F^{\mu v} + (m^2/4) \epsilon_{\mu v \rho}A^\mu F^{v \rho},$$ when I make a gauge transformation $A_\mu \to A_\mu + d\lambda$, the lagrangian changes by a total derivative, which we can change it to surface integral. We assume the total derivative term, which can be converted to surface integral, vanishes at large distances. If we don't assume this does this change the symmetries or does it change the conserved quantities (i.e change the momentum, angular momentum operator etc.)