Judging from the Google results I just got, these are apparently a mythical foodstuff among SF fans. No one's quite sure what they are, but most agree that they're decidedly unpleasant.
However, I know what they are, because I've read (or at least started to read) The Gripping Hand, by Larry Niven and Jerry Pournelle. Greeps are an alien species vaguely like crabs, but less aquatic. They are served live in local restaurants in a large shallow bowl with edges just steep enough to prevent them from escaping. You stab one in the neck with a crottling fork, expose the meat, and eat it while it's still moving. The scene in the book where the protaganist orders them is quite memorable, and culminates with the line, "So, wretched sand dweller! Now you will tell me of your troop movements!"

It's also my band name. So don't steal it.
The first appearance of "crottled greeps" seems to be 1953, used by Dean Grennell in a joke one-shot science fiction fanzine called Filler and containing nothing but short filler items -- "Filler 378" is quoted in several places as:
"But if you don't like crottled greeps, what did you order them for?"
Apparently, the origin of the words in the phrase is from the cartooning term "crottles," used to describe the little bubbles and lines drawn above a cartoon character's head to indicate that they are intoxicated; and an English-speaker's spelling of the French word "grippe," used in French and in the past also in English for the disease now called "influenza." In 1956, Lee Hoffman used the name to describe a "seductive but lethal viand" in a short story in another fanzine, Grue (issue #27). Many other stories used the phrase as a fun reference for dedicated fans to catch, and and at least one filksong. None of the stories until the 1990s really specified what, exactly, crottled greeps were. People's suggestions include:

In 1990, Greg Costikyan's "Another Day, Another Dungeon," took the running joke of no one knowing what crottled greeps were and ran with it; a fan review notes "Every time the characters stop for food, the food vendor tries to sell them greeps. The vendor would tell them his life story, complete with the story of the greeps. Strangely enough, every single vendor had a completely different species of greep. There were bird greeps, fish greeps, insect greeps, small furry greeps, and more." Apparently, though, the greeps weren't all served crottled.

In 1993, The Gripping Hand by Larry Niven and Jerry Pournelle topped the many fannish speculations by making the crottled greeps ordered by one brave traveler turn out to be live food:

The creatures in the bowl might have been four-legged crabs. Their sides pulsed. Renner remembered reading that they were land creatures. They could almost reach the rim before they dropped back. Their eyes were locked on Renner's as they climbed toward him. They looked hungry and determined.
"Pick up the crottling fork," Belinda whispered. "The two-pronged fork. Use your thumb and two fingers."
It was sitting beside the bowl. Renner picked it up. Belinda whispered, "Stab just behind the head plate. Do it hard enough to set the prongs. You don't want it to drop off."
Hesitating was bad: the greeps would move. You couldn't blame them. Renner stabbed one and lifted the fork. Belinda said, "Scrape it off on the edge. You didn't stab hard enough. They bite."
Renner scraped it off and tried another. The beasts weren't fast, but it wasn't easy to center the fork. He stabbed.
"Good. Pick it up. Your left hand takes the tail. Pull hard."
Renner pulled. The exoskeletal tail came right off, exposing two inches of pale meat.

Niven, Larry, and Jerry Pournelle. The Gripping Hand. New York: Pocket Books, 1993. https://books.google.com/books?id=YGALosQ3-DYC&pg=PA27&lpg=PA27&dq=crottled+greeps+gripping+hand

The solution proposed by Niven and Pournelle is unsatisfactory: it simply makes no sense. Firstly, crottled greeps implies they are greeps prepared by that particular method; yet the greeps arrive alive and apparently in their natural state. How then can one assert these to be an order of crottled greeps? Based on the story's explication of crottling it would seem more reasonable that such an order would arrive with the greeps pre-impaled and -tailed. Secondly, why would anybody invent the term crottling and thence crottling fork for what is a straightforward and ordinary stabbing, or spearing, or impalement, or any of the numerous other verbs available for this already ubiquitous action? This is an absurdity, and also has a whiff of circularity: it's called crottling because one uses the crottling fork, which is so called since one uses it for crottling, which... I find that the authors have simply dodged the essential difficulty (and potential) in the term, which is cheap and unimaginative.

However, their concept does contain the germ of a good idea. I propose the following, for the use of whatever hack should want to pinch it: the greeps in their natural state are too swift and too vicious to be dealt with as in The Gripping Hand; when prepared for table, therefore, they are presented live, but intoxicated with crottle, a herb which upon ingestion acts on a greep approximately as inhaled catnip does on a cat. This allows the spearing of the crottled greep with the (sensibly renamed) greep-fork and ideally also alters the flavor in an agreeable way (although one can imagine a variant where the effect on the taste is detrimental, causing real gastronomes to lament the necessity and even, perhaps, endeavor to contend with undazed greeps for a superior meal).

As you can see, this neatly solves the difficulty in the Niven/Pournelle original. The dish arrives crottled; crottle is justified as a species name just like greep, as well as retaining its original connection with intoxication from the world of comics; the repellent nature of the dish is retained and even enhanced by the implication that an uncrottled greep may fuck your shit up to an unspecified extent. Also, crottle has a fine ring of throttle, as an engine, and the German word Kräuter, meaning herbs: both clearly appropriate associations. (Concerning this last see also crottles.) In conclusion: it is self-evident that my solution is the best and my genius is superior.

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