Hey there mreaves311
Side shoots are perfectly normal so don't stress over it. I would suggest leaving the leaves on the plant, particularly if there are old pitchers on the ends of the leaves as they continue to absorb nutrients for a long time after the pitcher/ leaf loses color.
That shoot is not even close to being big enough to cut and replant so leave it be for the time being.
Some Nepenthes don't take well from cuttings but it will depend on the species, I can't see what you have as there isn't enough detail in the images. The deep green (which may be from a lack of light) and the decurrent leaves narrows things down but from what I can see of the pitchers it is likely a hybrid.
Cheers, Troy
