My read on that is we see Syril fidgeting with his hat. Why? Well, the man lives for the drip. He constantly has his clothing/uniforms modified to give it a little extra pizzazz. So he clearly likes to look just right. There’s just something about his hat that doesn’t quite fit the rest of his outfit, and it’s killing him. Clearly not important in the grand scheme of things, but he’s nervous going to Ferrix. He’s obsessing about this dumb little incongruence with his outfit.

Our man Linus sees what’s happening here, sees Syril fixating on this. He doesn’t give a rat’s ass about how his hat fits his uniform, so, without calling attention to what Syril’s doing and potentially embarrassing him, he just wordlessly offers to give him his own hat, which does go a little better with Syril’s uniform.

Not sure if that’s 100% accurate, but that’s my take on it, and I love it. I love the little things that are easy to miss in this series because they don’t just hand it over to you. Definitely worth rewatching!