Okay.

Technically, yes. If you wait a finite amount of time, and use several observable universes worth of energy to pull it out, you could. Whatever object would have to survive a lot of radiation.

But yeah, sure. Kinda. But it never crossed the event horizon.

The moment it crosses, physics doesn't work, and the object isn't an "object" anymore. It goes to a place where time and space swap places and it takes an indefinite amount of time to reach there. One of my amateur theories on the matter is that objects don't cross the event horizon, the event horizon "reaches up" to engulf objects at it approaches the black hole. There's not enough time in the universe for objects to pass the event horizon.

Now, if you wait until the CMB is colder than the black hole's hawking radiation, you might be able to see the energy of your object become hawking radiation, and when you pull your string, you get just the string. Pulling the string would still require the energy of observable universes.