Mechanistic logic: a competitive blocker is reversible by sheer mass action, so flood the synapse with acetylcholine by inhibiting cholinesterase.
Neostigmine, a quaternary-ammonium anticholinesterase, stays in the periphery and raises end-plate acetylcholine, displacing the non-depolarising agent and restoring neuromuscular transmission. It is co-administered with an antimuscarinic (atropine or glycopyrrolate) to prevent bradycardia and secretions.
Rule out the rest: physostigmine is a CNS-penetrating anticholinesterase used for central antimuscarinic toxicity, carbachol is a direct agonist for miosis in eye surgery, and succinylcholine is itself a paralytic. So neostigmine is the reversal agent.