Hard to know. Gharr still believes the fleet to be in orbit of Jupiter, so he wouldn't know that he can direct the communication towards the moon. I'm not sure of the capabilities and limitations on the fleet's ability to filter and sift through the comms as well but that could give them two things to consider.

1. A communication that can reach Jupiter with enough power and coherency left in the signal to deliver a message.

2. A communication the fleet would recognise as coming from Gharr and get flagged for inspection from among the plethora of other communication noise.

We've talked about the government possibly monitoring for odd communications and activity. If there's one thing I'd consider an alien trapped on the planet to be doing it would be attempting communication with it's fleet. I'd be keeping an eye on communications regarding transmission to Jupiter or outer planets and any purchase activity that could relate to equipment for that purpose.

Gharr isn't an engineer or a physicist, and the kids he's with almost certainly don't have access to the kind of technology they'd need to aim a laser at a moving target several hundred million kilometers away. I bet it won't be long before Gharr realizes that and decides it's time to turn himself in peacefully, betting on the likelihood that the fleet is watching.

Come to think of it, I've no idea what their backgrounds are. 25 year old Val is supposed to be somewhat sporty and enjoy the outdoors while 23 year old Dan appears to have some I.T. knowledge and possibly security if his talk at the campfire was about bypassing it at some facility. Mark is 29 years old but I'm yet to see much of an indication as to his profession or knowledge on things.

Regardless, they don't necessarily need a high power laser communicator to hit the Jupiter fleet with pin-point accuracy. The Alliance fleet was picking up signals from outside the system, let alone Jupiter. They only need to broadcast with enough strength that it can reach Jupiter in a coherent enough fashion for Alliance tech to pickup and interpret together with some method of ensuring the Alliance fleet would flag it among the many other random broadcasts being transmitted from Earth with enough power to be picked up. They also don't need to necessarily worry about making it two way. It could easily be enough to let the Alliance know simply Gharr's location. Gharr's own communicator in turn is likely capable of picking up signals, even if it doesn't have the range to respond and Alliance communicator equipment is likely strong enough that even if the fleet signal is picked up, it won't be anything they could interpret.

The other key would be for Gharr and friends to transmit the location in a way that couldn't be decoded by Earth military listening in. Their best bet would be using the strongest commercial encryption methods they can. Even if we presume there are secret, state of the art military computers capable of cracking such encryption, it would likely still take some days or even weeks while Alliance computers could likely crack it in an hour if not minutes.

If there's nothing abnormal about a general, strong broadcast, it might not even warrant suspicion enough to be assigned to the best decryption methods and there can be a lot of noise to filter through for signals you care about. I remember a guy who was an engineer for the Royal Danish Airforce in the 80's telling me how they saw a guy turn up to the base in a car with one of the first remote key locks. They recorded the signal his keys put out and then proceeded to retransmit it from their powerful, airbase transmitter and laugh as the man suffered problems with his car immediately unlocking after he locked it. Personally I always found it funny to think of the 80's Soviet Union, monitoring communications being broadcast from a Danish airforce base and trying to ascertain just what the repeating, simple signal could mean.

At which point we're talking about power limits (to prevent harm to humans standing right next to it) to publicly sold lasers, and dispersion in Earth's atmosphere. (Assuming that we're still talking exclusively about lasers, rather than - much less focused - radio.)

Why use Terran crypto in the first place? If the Alliance is at all used to encrypting their transmissions, it's a safe bet that Gharrs communicator is equipped with an en-/decoder subunit and holds appropriate valid keys to contact "the fleet". Add use of some Raharr coordinate system instead of the domestic WGS84 or whatnot and it should be ultimate gibberish to human SIGINT.

Why, it's a woodpecker, obviously.

I'm talking more general radio, I'm not sure if the limits of the standard power grid would prevent them getting a signal thats legible enough for the fleet's technology but if so then that could easily be an issue.

You're correct that Gharr's communicator and/or wrist computer would likely have sufficient encryption to frustrate any terran military. However that presents the new difficulty of interfacing Gharr's communicator or computer with Terran transmission technology. It would likely solve the issue of getting the Fleet's attention from among the flood of other radio signals it picks up though.

How readily they can rig this all up depends either on one of them having some electrical and/or signal know-how or Gharr's neural computer having some basic tech details built in or the ability to upload Terran schematics and present guidance and options they can readily follow.