The inflo is the bloom stalk; yours doesn't appear to have one, but yes, I do recommend cutting them off because the cutting will devote energy to blooming when it should be rooting.
Do not cut the bottom. A cutting should be well calloused before starting the rooting process.
It will take a little while before you see new leaves emerge. The cutting will only need heat - no water - during the rooting process.
Good luck!
