Step 1: Focus on the tarsal tunnel, the passage beneath the flexor retinaculum behind the medial malleolus.
Step 2: Its contents in order are the tibialis posterior tendon, flexor digitorum longus tendon, the posterior tibial vessels, the tibial nerve, and the flexor hallucis longus tendon. The posterior tibial artery clearly belongs to this list, so it travels deep to the flexor retinaculum.
Step 3: The remaining choices are anterior or superficial: the great saphenous vein is a superficial vein ascending in front of the medial malleolus, and both tibialis anterior and peroneus tertius are dorsiflexor tendons confined to the extensor retinaculum on the front of the ankle.
Step 4: Only the posterior tibial artery fits the tarsal tunnel.
\[\boxed{\text{Posterior tibial artery}}\]