I identify a point-symmetric structure in recently published VLT/MUSE velocity maps of different elements in a plane along the line of sight at the center of the supernova remnant SNR~0540-69.3, and argue that jittering jets that exploded this core collapse supernova shaped this point-symmetric structure. The four pairs of two opposite clumps that compose this point symmetric structure suggest that two to four pairs of jittering jets shaped the inner ejecta in this plane. In addition, intensity images of several spectral lines reveal a faint strip (the main jet-axis) that is part of this plane of jittering jets and its similarity to morphological features in a few other SNRs and in some planetary nebulae further suggests shaping by jets. My interpretation implies that in addition to instabilities, jets also mix elements in the ejecta of core collapse supernovae. Based on the point-symmetric structure and under the assumption that jittering jets exploded this supernova, I estimate the component of the neutron star natal kick velocity on the plane of the sky to be $\simeq 235 \km\s^{-1}$, and at an angle of $\simeq 47^\circ$ to the direction of the main jet-axis. I analyse this natal kick direction together with other 12 SNRs in the frame of the jittering jets explosion mechanism.