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But once it enters our gravitational system it’s future course will be unpredictably altered.

Actually, by that time the predictions will be pretty good already. The real problem for most of these reports is that people don't really understand the statistics.

Here's the process: We identify, usually by optical telescope, a body that is not fixed against the distant stars - hence it's an asteroid or comet (or dwarf planet, or moon, or whatever label you want). We take measurements of the apparent position. Each measurement has an uncertainty. On the basis of three measurements, we can compute an orbit. in this case, it misses both Earth and Luna.

However, then the astronomers start to vary the measurements within the limits of the uncertainty. All combinations (within some small segment each to keep the problem from becoming infinite) are used to calculate new orbits. Some of those (near the nominal readings) are higher probability and some (at the extremes of the uncertainty) are lower in probability. After all of these are calculated, an overall probability of impact (on Earth, or Luna as desired) is calculated.

The resolution to this is more measurements, and in particular measurements distant from each other. From that the range of options (within the uncertainty) is reduced. By the time it arrives in our area in 2032, the orbit will be pretty well defined.

The 'unpredictable' element is that (very) small differences within the remaining uncertainty in its actual orbit can still result in larger differences in the long-term orbit when a very large perturbation (getting near Earth or Luna) is added. But it will be quickly recalculated, and with much better accuracy than our current distant, close together, optical measurements.