So is it not attempting to eject at all? Watch the felt window carefully when you hit eject. Is it making a noise? Do you see the felt move at all?
Many times I've had customers bring in a liquid spilled laptop (and occasionally iMac...) that they had spilled pop and it got on the felt. It absorbs pop like a sponge. Then the pop dries out, leaving behind the sugar and syrup, and the felt is now very stiff and won't part easily when the (weak) eject motor tries to push out the disc.
Sometimes it just starts to peek out, gives up, and sucks it back in. If they just want their disc back I will boot into the boot selector, press the eject key on the keyboard, and as the disc reaches the outermost part of its travel (showing maybe 1-2mm of disc beyond the felt) and before it sucks it back in, I yank the power cord or turn off the power strip so the disc stays there. Then I get out an Xacto knife and dig into the lip of the disc and pull it out. The outermost ring on the disc is the last place to get written to so I'm not going to do any damage to the disc. But then again don't insert another disc! (tape up the slot)
Or you can takitapart and cut the felt off. Then it'll toss the disc out instead of just ejecting a bit for you to grab. Or you can pay for a new housing, and those (1) ain't cheap and (2) take a lot of time to replace. The felt is mounted on the outer shell of the laptop or bezel/rear housing of the iMac.
If you're quick you might even be able to snag it with a small needle nose pliers as it tries to peek out.
If it's not ejecting at all, no noise, the drive is defective. You will have to remove the drive and takitapart to get your disc back.
RARELY I ran into burned discs that were manufactured poorly with the hub ever so slightly too narrow and they tended to get stuck on the spindles. Sometimes a credit card could be used to coerce them out but often required takitapart.
In a way I'm glad to see ODDs are going away.
