Ban stored the broken Ant Mask, the Noble Moth Cloak and the Twin Baton inside the Dimensional Storage after inspecting them carefully. Aside from the Ant Mask, there's no visible damage that could be seen on his other items.
Ban also retrieved the 39 pieces of Elder Monk Tree branches from the Dimensional Storage before tying them up together with a thick vine. He was afraid that someone might see him carrying nothing whilst going to the city but still managed to complete his gathering Quest, so he chose to retrieve them early and just carry them openly until he arrived at the Adventurers Guild.
After they ate their fill, Ban and Eva immediately ran back towards the same path they used earlier. They passed checkpoints after checkpoints and it did not take long for them to arrive at the starting checkpoint, near the road that leads to Eagle City.