We study the evolution of debris created in the giant impacts expected during the final stages of terrestrial planet formation. The starting point is the debris created in a simulation of the Moon-forming impact. The dynamical evolution is followed for 10 Myr including the effects of Earth, Venus, Mars and Jupiter. The spatial distribution evolves from a clump in the first few months to an asymmetric ring for the first 10 kyr and finally becoming an axisymmetric ring by about 1 Myr after the impact. By 10 Myr after the impact 20 per cent of the particles have been accreted on to Earth and 17 per cent on to Venus, with 8 per cent ejected by Jupiter and other bodies playing minor roles. However, the fate of the debris also depends strongly on how fast it is collisionally depleted, which depends on the poorly constrained size distribution of the impact debris. Assuming that the debris is made up of 30 per cent by mass mm–cm-sized vapour condensates and 70 per cent boulders up to 500 km, we find that the condensates deplete rapidly on ∼1000 yr time-scales, whereas the boulders deplete predominantly dynamically. By considering the luminosity of dust produced in collisions within the boulder–debris distribution we find that the Moon-forming impact would have been readily detectable around other stars in Spitzer 24 μm surveys for around 25 Myr after the impact, with levels of emission comparable to many known hot dust systems. The vapour condensates meanwhile produce a short-lived, optically thick, spike of emission. We use these surveys to make an estimate of the fraction of stars that form terrestrial planets, FTPF. Since current terrestrial planet formation models invoke multiple giant impacts, the low fraction of 10–100 Myr stars found to have warm (>rsim150 K) dust implies that per cent. For this number to be higher, it would require that either terrestrial planets are largely fully formed when the protoplanetary disc disperses, or that impact generated debris consists purely of sub-km objects such that its signature is short-lived.