Just the two inch fiberous tubes that used to be the stems.

I kept the same worm bins going for years and when I finally dumped one entire bin the bottom section was full of banana stem strings as equinoxequinox mentions. These stings had loads of egg capsules intertwined in the stem strings. I no longer use the stems and I blend the peals along with the other kitchen scraps prior to feeding. There is very little residual food after two or three days.

I've been throwing food in whole. Without starting what can be a long and ugly thread; morgan you tend to like small particals when feeding and find they get converted quickest? How about particle size verses freeze/thaw to break down the cellwalls?

You can throw the stems back in if you find one not finished. I only rarely find a stem semi processed. But the thing is with the Inn, things seems to get processed all the way down and for longer as everything you pull out (unlike harvesting bins) is the oldest stuff you have. They do break down eventually.

I let banana peel sit in a bucket until they get really dark and soft and yuk before feeding them to the worms. I have noticed that some bananas lasted longer than others on my kitchen counter (didn't pay attention dole, chiquita or any other brand but not organic) and I believe this might be a result of spraying.
""How about particle size verses freeze/thaw to break down the cellwalls?"" Not sure which one is faster, interesting question that I've never asked myself. But both will definitely speed up decomposing.

Like PeterK2 I just throw any partially rotted stems back into the bin when I find them. Until I began worm composting I didn't know that banana stems were made that way - it's kinda neat.

mr_yan, freeze/thaw works just as well as blending. My only reason for not doing this is we have four freezers for storing garden surplus, game and fish...and not an inch of space to spare.

The freeze/thaw process will dehydrate significantly during the thawing process which may be a good idea for some. I blend my fruit and vegetable scraps using rain water or gravel syphoned aquarium water, and still I have to add additional water to the bins. My bins in the winter lay on a concrete floor in an unheated attached garage. In order to maintain proper heat the four bins sit on a carpet with a 6-ft long, heating strip from Growers Supply in between. This heater is operated with a toggle type timer which allows 15 minute on/off settings for heat control. The only problem with this is maintaining proper hydration which can get tricky if your not careful.