How are the orange wedges in prepackaged mandarin orange cups (such as
those sold in Wendy's kids meals) removed intactly from the fibrous
inner peel?  I can't manage that by hand, and they seem to have some
clever process that delicately removes the fibrous part on an
industrial scale.

lukachu,
I?m not familiar with the mentioned product, but if I understand
things correctly you are referring to a segment of an orange without
any pith or other outer membrane attached to it.

If this is the case the technology certainly exists and is composed of
a number of processes depended on the desired product. An excellent
description of a related process (removing pith from a orange) is
here:
http://www.freshcut.com/fc1999.htm#story43
under story name ?Fresh-cut Citrus: Beauty Is Skin Deep?

A further story alluding to the existence of segmentation processing is here:
http://www.freshcut.com/story43
under story name ?Growth "Dynamic" for UK Fruit Firm?

Unfortunately it appear the technology is commercially sensitive (i.e.
those that have it are making money out it) so fuller descriptions
have not been located in the time allocated, other than noting that
besides the obvious mechanics of the process, an essential element
remains computer management; resulting in it being largely autonomous.
A description of the importance of this has been found (I would
recommend against reading it, as it is technical by nature) here:
http://www.omimo.be/magazine/01q2/2001q2_p079.pdf

Kind Regards,
gfmaster