Step 1: Trace the tear pathway: punctum, canaliculus, lacrimal sac, then nasolacrimal duct, which drains into the inferior meatus of the nose.
Step 2: Guarding the terminal opening of this duct is a mucosal flap that functions as a one-way valve. This structure is named after Hasner, so the valve of Hasner is correct.
Step 3: The other choices belong elsewhere. Heister valve, which is the same as the spiral valve, lies within the cystic duct and regulates bile flow, so it has no role here.
\[\boxed{\text{Hasner's valve}}\]