As I note in the post, science fiction writer Arthur C. Clarke published what is as far as I know the first short story addressing this situation, in 1946. Loophole was published in Astounding Science Fiction:

From: President
To: Secretary, Council of Scientists.

I have been informed that the inhabitants of Earth have succeeded in releasing atomic energy and have been making experiments with rocket propulsion...

(Atomic explosions on Earth)

Equip an expedition to the satellite of Earth immediately. It is to keep a close watch on the planet and to report at once if rocket experiments are in progress. The greatest care must be taken to keep our presence on the Moon a secret...

From: C.B.E.P.S.
To: President.
Draft herewith:
People of Earth!

We, the inhabitants of the planet you call Mars, have for many years observed your experiments towards achieving interplanetary travel. These experiments must cease. Our study of your race has convinced us that you are not fitted to leave your planet in the present state of your civilization.

They had begun to realize that we were intercepting all their radio transmissions, and some messages have been broadcast directly to us. They state that they have agreed to ban all rocket experiments, in accordance with our wishes. This is as unexpected as it is welcome. Even if they are trying to deceive us, we are perfectly safe now that we have established the second station just outside the atmosphere. They cannot possibly develop spaceships without our seeing them or detecting their tube radiation.

The watch on Earth will be continued rigorously, as instructed.

(Read more at Alien Watch on Earth)

Henry Cobb responded by pointing out that "Our mightiest nuclear explosions can't be seen by ET", linking to a National Radio Astronomy Observatory (NRAO) article At What Distance Can We Detect a Nuclear Explosion in the Universe?, which concludes:

...a one megaton nuclear explosion (L = 4×10^(13) Watts) would be detectable with each measurement system above:

• Naked Eye: D ~ 1.8×10^(11) m ~ 1.2 Astronomical Units
• Hubble: D ~ 1.8×10^(16) m ~ 2 light years
• JWST: D ~ 5.6×10^(16) m ~ 6 light years
• 10m optical telescope integrating for many hours: D ~ 1.8×10^(17) m ~ 19 light years

This suggests that even the most powerful telescopes could only detect a 1 megaton nuclear explosion out to approximately four-times the distance of the nearest star (about 4 light years), and could not be seen at the nearest cluster of stars (about 153 light years). This also assumes that we caught the blast at just the moment that it exploded and that 1% of its energy was emitted at optical wavelengths. These are very optimistic assumptions, so the actual distances are likely to be much closer than the estimates above.

All this comes as a relief to me, ever since reading Cixin Liu's The Dark Forest (2008), his followup to The Three Body Problem (2006):

“The universe is a dark forest. Every civilization is an armed hunter stalking through the trees like a ghost, gently pushing aside branches that block the path and trying to tread without sound. Even breathing is done with care. The hunter has to be careful, because everywhere in the forest are stealthy hunters like him. If he finds other life—another hunter, an angel or a demon, a delicate infant or a tottering old man, a fairy or a demigod—there’s only one thing he can do: open fire and eliminate them. In this forest, hell is other people. An eternal threat that any life that exposes its own existence will be swiftly wiped out. This is the picture of cosmic civilization. It’s the explanation for the Fermi Paradox.”