Since landing on Mars, the NASA InSight lander has witnessed eight Phobos and one Deimos transits. All transits could be observed by a drop in the solar array current and the surface temperature, but more surprisingly, for several ones, a clear signature was recorded with the seismic sensors and the magnetometer. We present a preliminary interpretation of the seismometer data as temperature-induced local deformation of the ground, supported by terrestrial analog experiments and finite-element modeling. The magnetic signature is most likely induced by changing currents from the solar arrays. While the observations are not fully understood yet, the recording of transit-related phenomena with high sampling rate will allow more precise measurements of the transit times, thus providing additional constraints for the orbital parameters of Phobos. The response of the seismometer can potentially also be used to constrain the thermoelastic properties of the shallow regolith at the landing site. Plain Language Summary The geophysical lander, InSight, has been operating on the surface of Mars since November 2018. Since then, the Martian moons Phobos and Deimos have been partially blocking the Sun, as seen from the InSight landing site, multiple times. Multiple InSight instruments have been measuring the effect of those transits; this surprisingly includes the seismometer and the magnetometer. We conclude that temperature-induced deformation and tilt are responsible for the seismic measurements. The change observed in the magnetometer measurements are most likely the result of a drop in the solar array currents. We do not observe atmospheric modulations with InSight's weather station during the transit. These observations help constrain orbital parameters of the Martian moons, and the seismometer signal might allow investigating thermoelastic properties of the shallow Martian material.