The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole of the size of the coherence length is considered. While the neutral zero energy Majorana core state remains intact due to its topological origin, the energy of charged excitations is significantly enhanced compared to that in the unpinned vortex. As a consequence of the pinning the minigap separating the Majorana state from the charged levels increases from Δ2/E F (EF is the Fermi energy and Δ is the bulk p-wave superconducting gap) to a significant fraction of Δ. Suppression of the thermodynamic and kinetic effects of the charged excitations allows us to isolate the Majorana state so it can be used for quantum computation. It is proposed that thermal conductivity along the vortex cores is a sensitive method to demonstrate the minigap. Using the Butticker-Landauer-Kopnin formula, we calculate the thermal conductance beyond the linear response as a function of the hole radius.