They have all the influence over it. They had choices -- deal with the thieves guild or go off to the distant adventure site -- and they chose to ignore the thieves guild. The state of the city on their return is based on the decision they made.
Do you think the world should freeze in place as soon as the PCs move out of view, like in a video game?
Because as far as the players are concerned that’s exactly the way the world works. The thieves guild isn’t a “consequence”. It’s a plot hook. It’s no different than a dragon moving in or a thousand other plot hooks. The only reason they matter now is because the dm decided to make them matter.
As far as the players are concerned, they had zero input into this. It’s an interesting adventure sure. No problems with that. And frankly that’s how most games work.
But this pretense that it’s some sort of “living world” or “consequence” is just smoke and mirrors. It’s a convenient fiction that dms tell themselves so they can sneer down their noses at games that actually actively allow the players to determine these sorts of things.
Imagine instead that the you have a side game played over email or Discord between sessions where each player controls a faction in the town and the reason that the thieves guild has become dominant is because of how that side game played out.
Now the players are actually directly engaged in the events of the town. That’s what a “living setting” looks like. Dms simply dictating results isn’t a living world at all. It’s fanfic writing.