Magnetic vortex cores are interacting with and can even be annihilated by artificial defects, such as holes. These defects have been fabricated by focused ion beam milling (FIB) into the magnetic domains, domain walls and the center of square-shaped vortices, known as Landau structures. We report the imaging of the magnetization dynamics of Landau structures containing holes by means of x-ray magnetic circular dichroism photo-emission electron microscopy (XMCD-PEEM). Due to the high lateral and temporal resolution of this method, the magnetic excitation spectrum, which is characteristic for the vortex-hole interaction, is investigated in detail. We find that the vortex core as well as domain walls can be trapped by small holes. With the help of micromagnetic simulations we show that the vortex gyrotropic motion frequency is enhanced, whereas the amplitude is significantly reduced in the case of non-centric holes in domain walls.