I can't see any screws and it seems like rigid plastic all around. The only thing I can see that look like they could come undone are the grey pins but they seem quite firmly in place...

I've since sold my ex495, but from what I remember... One side (I think the right) is more "bendable" than the other. You simply pull it to the side causing the pins to disengage, then pull the drive up from that same side, then remove the tray.

The details are probably covered in the manual.

Yep.
It is in the manual.
http://h10032.www1.hp.com/ctg/Manual/c01868379.pdf
7.Insert the new drive into the left side of the hard drive tray, making sure that the pins go into the hard drive’s mounting holes.
8.Flex the right side rail, and then insert the pins into the hard drive’s mounting holes.

So reverse that above to remove.
If you are not replacing it then you need to fold the flap in the back up again.

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Got it based off what you said, thanks

I have several PDFs for this thing all in different places - I wouldn't know where to start looking!