I was just wondering what are the chances that there is a small object (say less than 1 km but more than few meters) that orbits the Earth but has remained undetected by us? Are we actually scanning the space around the Earth continuously for orbiting bodies?
One kilometer, no way! That would've been known since long ago. Most asteroids of that size have already been found, all the way out to the asteroid belt beyond Mars. Earth has no second Moon. But there are always some tiny asteroids around, which are temporarily captured by Earth's gravity. Here's a funny illustration of such an orbit, it is not what we would like to call a moon. I think that only one of them have been found, the 5 meter diameter 2006RH120. Smaller objects would not be detectable today, but there are at any moment likely many meter and submeter sized asteroids visiting the Sun-Earth Lagrange points. A paper about it.
Space is not yet being scanned, but telescopes are now being built to do that. It will be a new kind of astronomy, looking for the unexpected, and who knows what will be found out there in the blackness. Still today amateur astronomers can discover asteroids with the telescope in their backyard. I'm afraid that space telescopes like Gaia will kill their hobby and that this classic astronomical mapping of the sky will finally be finished.
The chances of what you are suggesting are almost nil. Though we might be constantly scanning our surrounding atmosphere to detect fragments of, or actual meteorites, other than the debris and artificial satellites that we ourselves have put in orbit around the earth, there is no second moon currently in orbit around us to the best of our knowledge.
There is, however, a theory that proposes the presence of another moon in the past. As per this theory, there was a planet "Theia" immediately close to earth that underwent a close collision with Earth to form two moons, which ultimately coalesced to form the single moon we see today.