He continues to watch Bucky's reactions as closely as he can, trying to piece together a man he only hopes to get to know better here and back in his own world. This Bucky who's survived the horrors of his past, no longer the weapon Hydra turned him into.. This man gives him hope for his own Bucky's recovery.

The comment gets a good natured smirk out of Steve "Saw some houses back there, figured there's some trashcan lids that'll make due," the playful tone says he knows how ridiculous that is, but doesn't care.

He's so much more comfortable armed with his fists or a shield, the axe would just get left behind at some point if Steve kept it. If Bucky can find a use for the axe, then he can have it. That or give it to Thor.