Sollux captchalogued the gun in his sylladex, not putting it in his strife specibus. He had no desire to wield it as a weapon. He just wanted to make sure Eridan couldn't get at it, and with the encryption on the card, even if he could somehow take control of his sylladex (lol) he wouldn't be able to get at the gun.

Then he stepped back almost to the door, and let Eridan down.

"You can get thith back when you prove to me you can behave like an adult troll, inthtead of a pthycotic freak," he said.