Jesper's grin is automatic and he turns his chair around to face Sylvain, reaching out his hands and scrunching them toward him as an obvious 'come here' gseture.

"An always welcome one, darling, but lock the door behind you."

It's not as if they are going to immediately do anything but it seems wise to do it now, before that ends up happening. That's the thing with new lovers, it's an easy as a particular smile and raise of an eyebrow. He also doesn't want Inej to walk in on them, and she's well aware what a locked door means for him. He would put a more obvious sign on the door but he doesn't want Kaz to notice.