Not too much. It's just a single ton. Unless it's a ton of antimatter

I've been curious about this subject (increasing or decreasing the planet's mass) & wanting a real fact based explanation. The fact that man has built structures that had a measureable impact to Earth's tilt indicate that there is a calcuable figure that represents the effect that the cumulative mass being removed from close to Earth's core/surface & shifted into orbit or pushed out of the planet's gravitational field has/will have. I've got no idea ehat the impact would be, but at some point reducing the mass of a spinning object has to result in changes. How many non-returning ships sent off-planet does it take to reduce the gravitational field of Earth? Does it impact Earth's orbit around the Sun? And inversely, how much off-planet mined materials brought here before ...idk - Earth's gravity is increased? Assuming the # is "real", shouldn't we be determining how much can be mined on the moon & brought here? Better now than waiting until the next environmental crisis headlines read "Moon weight loss has lead to extreme ellipse-ing of it's orbit: expect even more monumental tidal extremes!". Again, I don't know what the real impact would be, I made this last bit up for dramatic effect/illustrate my question.

There isn't likely to be much material shipped down the gravity well. It's too expensive unless you can also build a space elevator, and maybe not even then. Maybe for some very high value metals, like platinum. Otherwise, the value of the metal has to be greater than the value of the heat shield that you're going to ablate away on entry.

Asteroid mining is very useful for building things in space. Not so much on Earth.