From what I know of Githyanki lore from playing D&D for a few years now, they should react in some way. They are an extremly xenophobic race and seeing someone, who is a lesser being in their eyes, wearing one of their armors should provoke a reaction.
Lae'zel makes pretty clear, how gith see other races: underlings and servants. Therefore it is not far fetched that they would be offended by servants wearing the masters armor.
It wouldn't Chanege the encounter much, since the gith hate us anyway, but it would show, that npcs react to stuff, which makes the world more alive.
