As the current moon spiraled out to its current position, it would have either collided with the moons, ejected them, or locked them into resonances. If it locked them into resonances, their semi-major axes would have expanded as the Moon's orbit expanded until they were stripped away by the Sun. So basically, the same as being ejected except with a time lag. This is my guess by the way, but it's interesting so later I'll try to simulate this.

If they were thrown out of Earth orbit, their independant orbits around the Sun would be Earth-crossing, and ultimately they'd collide with the Earth or Moon with hyperbolic velocity. It's unlikely that they could survive in an Earth-crossing orbit for billions of years.

This could be a source of the maria on the Moon. These objects would orbit the Sun for a few million years while the Moon's surface solidifys, enabling it to preserve the scar of an impact of a large object.

Something I've wondered is what happened to the other proto-moons that made up our Moon. All the debris in Earth orbit from the collision with the Mars-sized object formed many small moons that merged together into bigger and bigger moons until one dominated and sucked up all the others. But when it approached its present size, it had enough gravity to eject competing moonlets from the Earth / Moon system. So for a few million years, there should have been some moonlet-sized objects orbiting the Sun in Earth-crossing orbits. Maybe their ultimate fate of an Earth or Moon collision created the maria.

Interesting question.