You've gotten pretty poor answers so far. I suspect they'd try to communicate in a wavelength where there is little interference. It's one thing to notice "there is a tiny amount of wavelength X light from the vicinity of alpha centauri" and a whole lot harder to notice the difference between two light sources close together at the same wavelength. The latter requires sensitivity to magnitude AND incredible angular precision. It's like seeing a flashlight from a long way off even though you couldn't make out an object that size in daylight. You know the flashlight is on, but you can't resolve it spatially.

We wouldn't be able to see the probe itself, rather we'd see its laser. The planet outputs (or reflects) vastly more total light than the laser, but the laser is pointed directly at the receiver and can output more light in that specific direction than the planet does. Plus, to get interesting data about the planet we need to get quite a lot of light from it, whereas we can get data from the laser over time by pulsing it so long as we can get any light from it at all.

'Seeing' the probe is like being connected to the internet.

Your friend in Japan can take a picture of an apple and email it to you in the US. Your friend's camera is like the camera on the probe.

You can't see the apple from where you are, but your computer can 'see' the internet.

Your friend uses the internet to send you a digital code that your computer turns into a picture of an apple.

The optical systems used to meld the output of the lasers could be used in reverse as a vast and sensitive telescope.

But why would we be unable to see the star's planets if we are able to see a probe that small?

The laser receiver might be able to see the planets in question, but a probe with an interstellar worthy camera in the direct vicinity of the planets would obviously be able to capture a much higher resolution image.