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Garnet scintillators often suffer from undesired afterglow, the origin of which is not always well-understood. A possible origin is contamination with transition metal (TM) ions. These impurities can act as traps giving rise to afterglow. Alternatively, they may show long-lived (microsecond) d-d emission. Here we present a systematic study on the role of 3d TM impurities in (Lu,Gd)3(GaAl)5O12 garnet scintillators. Scintillator disks intentionally doped with ppm levels of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, or Zn were studied to identify TM-related traps in thermoluminescence (TSL) glow curves and their role in afterglow. For Ti, V, and Cr additional TSL peaks were observed that gave rise to RT afterglow in the 10-2-103 s time range, depending on garnet composition. On the millisecond time scale long-lived red/near-infrared emission was observed from Mn and Fe impurities, explained by spin-forbidden d-d emission. We show that afterglow can be reduced by the use of ultrapure raw materials. Other solutions include bandgap engineering for the garnet host to modify trap depths and applying optical filters to block the spin-forbidden d-d emission. The present study provides an insightful overview of the role of 3d TM impurities on afterglow in Ce-doped scintillators and procedures to predict and reduce afterglow. These insights will aid the development of Ce-doped garnets with superior afterglow behavior.