This scenario doesn't happen in the mainline Pokémon games. Here's why:
* No Specific Character: There's no specific female character in the Pokémon games who gives you a squirtbottle after defeating a gym leader.
* Squirtbottle's Purpose: Squirtbottles are used primarily in the early stages of the game to catch Pokémon by weakening them. By the time you're facing the third gym leader, you've likely progressed beyond needing to use a squirtbottle.
* Gameplay Focus: The Pokémon games focus on battling, exploring, and catching Pokémon. There aren't many side quests or interactions that involve unique items like squirtbottles being given out at specific points in the game.
Could this be a Fan Creation?
It's possible you're thinking of a fan-made game, a modified version of a Pokémon game, or a fanfiction where this scenario occurs. If you can provide more context about where you encountered this idea, it might be easier to understand what you're asking about.