[X] Settle back down and prepare yourself to evaluate District 4. (If you want to survive the opening day of the games, you know you should probably learn everything you can about the career pack. Honorius knows 2 like the back of his hand and will probably try to help you get an alliance with 2 or 4. You don't have anything against Willow, you might even try to ally with her in the arena, but there can only be one winner and you need to cover your bases.)
Only 1 person can win the Games. If the Quest's goal is to win, whether we reach out to Willow or not doesn't matter (the aimed for end goal is her dead regardless).
Staying guarantees Honorius does more than make the bare minimum effort (just projecting- that could mean anything from better training, or getting a chance to make alliances with the careers). Leaving means we leave that to chance.
And besides- We made an effort before, she said no. What makes you think the response will be any different now?
Who knows maybe she actually has a good reason for what she did.
Distrust and hate for Honorius as a 2 (understandable). Hatred for the Capitol and not wanting to play their game (equally if not more understandable).
Some semblance of pride and fatalism — she's probably already accepted that her odds of not ever going home are, well,
high. And if that's the case, better to die while remaining true to yourself.
Pride and grief could also be reasons. Mix and match, et cetera, et cetera.