  Seven of the nine known Mars Trojan asteroids belong to an orbital cluster
named after its largest member 5261 Eureka. Eureka is likely the progenitor of
the whole cluster, which formed at least 1 Gyr ago. It was suggested that the
thermal YORP effect spun-up Eureka resulting with fragments being ejected by
the rotational-fission mechanism. Eureka's spectrum exhibits a broad and deep
absorption band around 1 {\mu}m, indicating an olivine-rich composition. Here
we show evidence that the Trojan Eureka cluster progenitor could have
originated as impact debris excavated from the Martian mantle. We present new
near-infrared observations of two Trojans (311999 2007 NS2 and 385250 2001
DH47) and find that both exhibit an olivine-rich reflectance spectrum similar
to Eureka's. These measurements confirm that the progenitor of the cluster has
an achondritic composition. Olivine-rich reflectance spectra are rare amongst
asteroids but are seen around the largest basins on Mars. They are also
consistent with some Martian meteorites (e.g. Chassigny), and with the material
comprising much of the Martian mantle. Using numerical simulations, we show
that the Mars Trojans are more likely to be impact ejecta from Mars than
captured olivine-rich asteroids transported from the main belt. This result
links directly specific asteroids to debris from the forming planets.
