Hi, for the past few weeks, my CLD-D925 has been leaving grease spots on the discs.
However, I can’t figure out where they are coming from.
Does anyone have any idea where it could be coming from?

Looks like its coming from inside the player.

Have you opened the player up?

I would assume someone over-greased the sled at some point recently. It’s probably wiping it clean during side changes when the laser moves quickly back to the center after side 2 is done.

I’d open it up and look inside at the rail. Maybe just wipe it with a small paint brush to collect the excess.

Thanks everyone for the help.
I found the cause. It are the cushions in the disc tray.
They were dirty or are starting to decay. I'll keep an eye on it.

No I don't think so, you need figure it out.
Those cushions aren't that thick, unless they somehow sucked up a bunch of liquid before you received the player.

You can replace if needed but I own players older than yours without any of these issues.

I rechecked the laser assembly. It is almost dry and needs to be lubricated. It are the cushions, the top one (photo). I have slid a laserdisc against the cushion and it made a greasy stain. What material can I use to replace it? felt, foam?

Look at the ones in the 8-inch disc part of your player's tray, they may not be damaged, and you can probably see the original height of the "dots". Probably 1mm above the plastic surface or similar. Then, entirely remove one of the bad ones to see the thickness of the recess below the tray surface, also likely 1mm or so. There are likely many choices for 2mm-thick rubber "feet"/pads with adhesive back surfaces, or adhesive rubber sheets, and you could cut out circles that will fit. I doubt that the material is critical, they are mostly just to protect discs from being scratched by the tray surface.