Help a working girl collect her fee.
Scarlett should visit the Ambrosial Lotus in the Arsenal District. The Lotus entrance is on the main level (same as the gate to the Inner City) and can be found by passing through an arch that runs under the stairs (walk past the stairs without climbing them.)
Speak with Venus, one of two scantily-clad working girls in the common room. She will complain about a customer who stiffed her.
Scarlett may either pay Venus immediately and then go collect the money from the Venetian Captain (assuming Scarlett has 150 ducats), or Scarlett can collect the money from the Captain first and then bring it back to Venus.
Speak with the Venetian Captain and demand payment on behalf of Venus. Threaten to speak with his superiors if he doesn't pay. He will provide the Ducats. (Note that although a "health bar" appears over the captain, it doesn't appear to be possible to pick a fight with him.)
Return to Venus at the Ambrosial Lotus to complete the quest.