Rare-earth materials epitaxially codeposited with III-V semiconductors form small, spherical rare-earthmonopnictide nanoparticles embedded within the III-V host. The small size of these particles (approximately 1.5 nm diameter) suggests that interesting electronic properties might emerge as a result of both confinement and surface states. However, ErAs nanoparticles do not exhibit any signs of quantum confinement or an emergent band gap, and these experimental observations are understood theoretically. We use ultrafast pump-probe spectroscopy to investigate the electronic structure of TbAs nanoparticles embedded in a GaAs host, which were expected to be similar to ErAs. We study the dynamics of carrier relaxation into the TbAs states, which essentially act as traps, using optical-pump terahertz-probe transient absorption spectroscopy. By analyzing how the carrier relaxation rates depend on pump fluence and sample temperature, we conclude that the TbAs states are saturable. Saturable traps suggest the existence of a band gap for TbAs nanoparticles, in sharp contrast with the results for ErAs.