CD-i member CD-i Fan shares some detailed pictures of the caddies that are used to insert a CD-i disc in the CD-i 180 set and most CD-i 60x players (except for example the 605T which was equiped with a tray (hence the T at the end). The caddy was used to guide the disc on the spindle inside. You push it in fully and extract the clear plastic bit, but there's a sort of "guide" bit around the disc that stays in the player it's just guiding the sides of the discs and without the transparent case the disc will fall down. You pull the transparent bit out of the player after inserting. To get your disc back you put the transparent case back in and pull out the full assembly, according to Retrostuff, Jorne and TwBurn. As CD-i Fan observes, these caddies were not common 'Plextor' caddies that were available at that time. Where did these come from? Did Philips designed them internally? Or perhaps the Japanese Kyocera, who developed the CD-i 180?
[Thanks, CD-i Fan, TwBurn, Jorne, Rosewood]