Some TMNT stuff was always meant for grownups.
As a young boy Chet had bought four baby turtles and was with them on the way back home when a young man helped a blind pedestrian unexpectedly dodge a truck, the glass with the turtles was knocked out of his hands by a canister that fell from the truck. The baby turtles went along with the canister into a nearby open manhole cover and got lost in the sewers.
Chet didn't see his turtles again, but in the years that passed since then, he always had strange dreams in which they appeared to him as mutants. He is not seen again until the Turtle Soup short Fifteen Years Later, in which a grown-up Chet - working in New York sewer sanitation - encounters the pets he lost all those years ago, satisfied that they survived.
The name "Chet" pops up quite a few times in the Mirage Comics. There was really no reason other than the fact that, for some reason, at that time, Kevin Eastman and Peter Laird found the name humorous.