Insect crawled in between LCD display and backlight on iMac 27". How can I fix it?

So you don't need to worry about feeding it. :-)

If the iMac is a 2012-current model, there really isn't anything that can be done other than replacing the display, the display and the glass are fused together therefore they cannot be separated.

If the computer is a 2011 or earlier model, you can remove the glass with suction cups as they're held on by magnets. Once the glass is off then do not touch the display with your fingers otherwise you will get oil on the display, use a tissue or a small vacuum to remove the insect's body.

If you aren't sure what model year the computer is, click About This Mac and that info will be revealed to you.

Short of removing the glass or hoping the bug will eventually decompose and fall down out of sight there's not much you can do.

FWIW, I should have said "display" not "glass". I haven't had my afternoon nap.

Dead bugs cannot be fixed, not without divine intervention anyway.