Ooh, a toothy question, with some good answers already. But I think there's more fat to be chewed here yet.
As you've established from other answers, some "alphabets" encode entire word stems in single characters. Others, single phonemes. Others, single bits of information.
All of these can encode the same words of the same language. They just work at different "transport layers" (https://en.wikipedia.org/wiki/OSI_model).
And that's the problem. MEssages, and the alphabets therein, don't come from nothing. You aren't going to get a scientist poring over an "alphabet" without first poring over a whole lot more. Communication is a layered activity, and any scientist will be looking at the communication in terms of those layers.
So exploring the layers here may be informative, though the OSI model assumes bidirectional communication, so isn't ideal here.
At the bottom layer, we have the physical layer. This is the layer that user @blahblah suggested investigating: the "how the data got to Earth" layer. This is the "carrier", perhaps a radio wave, perhaps a metal plate found in a space ship, perhaps a strip of ferrous metal.
Next layer up, we have how that carrier was permuted to have a signal encoded onto it. Radio waves are not, by themselves, any kind of bits, characters, DNA, picture, or anything like that. How did they encode the signal on their carrier? AM? FM? Some other thing? If it was a metal plate, were characters etched into it, scratched, cast, stamped, painted on, glued on...? If it was a ferrous strip, did they reverse the magnetism at set periods in lines and columns (how our magstripes work), or did they arrange the magnetic regions in some other, more complex pattern? All this tells us something about the technology that transmitted it.
And how fine are the details? If they vary over multiple seconds, that tells different things than if they vary over nanoseconds. A microfiche slide is at a very different scale than a rune-carved dolmen; GHz radio comms are very different from manual morse code telegraphy; and data density on a modern hard drive platter is very different from that on a credit card strip. This doesn't give an upper bound to their tech level, but it gives a lower one, and also shows how far they hoped their message to go (in general, you speak slower and louder to be heard further away).
And what data correction did they have in their protocol? Was it just "if we repeat it enough times, it'll get through"? Or were there checksums and other error correction?
Given how they permuted the physical layer, how did they encode the data? Bits, for binary or morse-code type communication? Continuous analog levels, such as we might use for brightness levels in a TV raster image? Unique values, for words or characters?
And there can be many levels of encoding of the signal. Perhaps the signal, once decoded, builds raster images of characters. Perhaps the signal has unique values, each one of which maps to a character. Perhaps the signal is a sequence of commands which, when executed correctly, generate the characters.
Perhaps it's a bunch of bits or trits that need to be assembled according to some pattern into characters, which in turn need to be gathered into words, which in turn need to be gathered into phrases, which in turn need to be decoded as commands, which in turn need to be... you get the idea.
And you see there that the alphabet that was used to encode the words of he phrases of the commands is just another layer of encoding, like all the others.
So perhaps, to judge a language, we should look at a level other than the alphabet. Words, perhaps? The size of their vocabulary? But can even that help us? I do not believe so.
The highest level I think you can get in language is the statement, command or instruction. "Give me all your money". "It is sunny today". That kinda thing. Most human languages contain an infinite number of these.
Now I'm gonna make a logical leap here and say: any language can describe any concept. That's a big idea. You often hear "there's no way in English to say the concept X", where X is something like schadenfreude or whatever. Now, ignoring for the moment the fact that schadenfreude is totally an English word now, you'll note that the dictionary entry for it defines the word in English. So while in some language there may not be a native term for "blue", you can damn well bet there's a native phrase that can be used to describe blue.
Let's look at the field of computing. It has been shown that any system which is Turing complete can do anything that any other computer can do, including evaluate any arbitrary algorithm.
And there is a set of computer languages which have a minimal instruction set, languages such as brainfuck (8 instructions) and JSFuck (6 instructions). These languages have been shown to be Turing complete.
Therefore, any mathematical, logical or algorithmic concept can be imparted using a vocabulary of just 6 instructions. I'm not going to say this is equivalent to a human language, but it distills a truly vast area of human discourse down to 6 commands.
Therefore, I'd argue, vocabulary size won't tell you anything either. Even things like whether it complies with Zipf's Law don't tell you anything like whether it's a constructed or natural language or anything, since that arises from the way the language is used, not from how it was created.
So overall, I think that your scientists are going to be focusing on the information they can get from the "metadata", the "how it was done", rather than the actual message itself.
Note that until/unless the message has been deciphered, the readers of the message cannot tell that this layer was stolen tech. Perhaps not even then, unless the message explicitly says so.
Even then, they have no way of knowing where along the chain of communication layers the "stolen" stuff ends and the "stuff they are doing" starts. Did they steal the radio transmitter? The error correction mechanism? Did they steal the encoding? The alphabet? The language? We have historical examples of all of these on Earth, so we know all are possible.
Even if the stolen parts are clearly marked as such, it still tells the scientists information about the societies that the scavenger-culture has access to, so it's still valuable and will still be studied. Not only that, but it tells the scientists about the sending society that they can use the tech, so again, still useful.
