Well, to kinda answer my own question, I wasn't comfortable with the idea of anything fuzzy continuing to be in the tank with Chicory, so I pulled the plant, popped off the offending "banana" with a pen, rinsed the plant off, and put it back in the tank. There is some gravel lodged in the rest of the banana cluster, guessing that even tho it wasn't buried when I bought it, the store probably had it buried for some length of time, which apparently isn't good for them and can cause rot.
no more than 1/3 if you want to keep the bananas. fuzzy is bad. cut off and offending fuzzy bits with a sharp razor. do this in wholes. ie, leaf is fuzzy, cut off entire leaf. a " banana" is fuzzy, take off the banana.
I think this one must have been poorly handled. My original has added a couple of leaves, my second is shooting up its first new leaf. This one - the biggest leaves went pale and the one banana went bad. BUT now shorn of the bad banana and a few days of being loose in my tank, the newest leaves on it are greening up a bit. So hopefully it will pull through. Chicory has already taken to resting on the leaves.
And now there's a 4th one in quarantine waiting to be put in Lavatail's tank as soon as I upgrade him to his bettabow.
So far I've had to shear off two bananas, but it looks like the plant is going to be fine. It's latched into the gravel with a long root and it's putting up a new leaf. This leads me to believe that banana plants must be incredibly easygoing aquarium plants, because that's one for each of my 4 tanks and I haven't killed any, even the apparently sick one! (Yet)
Kinda neat the way they fasten themselves down. I looked at my original and oldest one last night and saw that it had battened down its own hatches.