The Immersed Boundary Method (IBM) has proven to be a valuable tool for the investigation of fluid-structure interaction due to its capability of dealing with complex geometries and deformable bodies. In particular, the IBM - Moving Least Squares (IBM-MLS) formulation exploits MLS transfer functions to interpolate flow quantities from the Eulerian grid to the Lagrangian markers, and vice versa, resulting in low oscillations on the hydrodynamic forces. Therefore, IBM-MLS is widely used to study flows with moving boundaries, such as biological flows. However, it has been noted that in some cases the resulting no-slip condition at the wet tissues is inaccurate, mainly due to the non-reciprocity of interpolating and spreading MLS operators. Therefore, implicit or iterative approaches are needed to reduce such error, thus significantly increasing the computational cost of the simulation. In our work, we propose an explicit correction for IBM-MLS that mitigates spreading and interpolating errors at each Lagrangian marker and correctly enforces the boundary condition on the IBs. Importantly, the local nature of the correction ensures the proper balance between the Eulerian and the corresponding Lagrangian IB forcing for each marker. The proposed correction is then tested and compared against standard IBM-MLS (also in its iterative fashion) in a series of benchmark flows, including fixed and moving rigid bodies. Lastly, the proposed method is applied to the FSI case of hemodynamics within a pressurized and deformable aorta.