[At the question, Byleth immediately went into 'protect food' mode, tugging the plate closer to himself and narrowing his eyes at her, as if expecting her to lunge for it like some ravenous beast.]

...there's still food on the table. Why are you- oh.

[His suspicious squinting immediately eased as he realised the stranger wasn't carrying a plate, and they were first come, first serve in that respect. An easily solved problem: he plucked the last of his food - three skewers - to hold them, and held out the plate to her.]

Was it the plate you wished for? Take it. I'll eat with my hands.

[He only grabbed a plate because people kept giving him looks for eating right off the table, but it didn't bother him enough to deter his appetite.]