I would get it out, since it's better to just assume something is bad, get it out and then not worry about the "what" part. Sometimes seemingly harmless things can mold or cause other problems down the line. The way it looks in the setup, it should be easy to remove with a bit of patience and time [do it carefully, since you don't wanna freak out the colony and have them run away, trust me it sucks]
This. If you can get it out easily with little effort there's no reason not to do it. It's most likely harmless but why take the risk if you can just remove it.
I'd also recommend you to put straw through the cotton (basically between the glass and the cotton) and put the tube into a small container/outworld.
This makes feeding them much easier. Also note that honey inside a moist tube can and will spoil after some time, if you feed them within the tube best put it on a piece of tinfoil or plastic so you can easily remove any leftovers. And be careful with large drops of liquids - smaller ants are really really good at drowning in these. Q-tips soaked in sugar water/honey water are a good way to offer liquids to ants that are prone to drowning.

Edited by Serafine, April 13 2017 - 2:26 PM.