“the dog found its way home”
Find one's way means to navigate to a destination. Find its way home describes the lost dog reaching home by itself, the scene that made Tina cry.
A2-48 / CEFR A2 / EPISODE 48
Sharing thoughts about a moving film
SceneAfter watching a moving film with Sarah, Frank and Tina talk outside the cinema.

WORDS & CONTEXT
Find one's way means to navigate to a destination. Find its way home describes the lost dog reaching home by itself, the scene that made Tina cry.
Sniffle means to make small sounds by drawing air through the nose, often while crying. Tina was doing this throughout the ending.
Dust is fine dirt in the air, and tissues are paper tissues. Frank blames his red eyes on dust to hide the fact that he cried. Tina points out that he used half her tissues, showing she already knows. It has nothing to do with problems with the stitches on his face.
Without ... means not having something. Here Frank suggests choosing a movie with no dog in it. He admits that he cried, but sets a condition for next time: avoid tearjerking dog stories. It does not mean "don't bring a dog to the theater." The punchline also connects to A2-03, where Frank admitted crying at a TV show and was embarrassed.