Nonrewritable tape?
This comic refers to Candy Buttons, a type of candy sold by Necco in the U.S. since 1980. Because they were glued to paper, each candy button would have some paper stuck to it. As said in the comic, some kids would carefully check each candy button to make sure they would not accidentally eat paper, while some kids didn't care and ripped them off, eating large scraps of paper in the process.
Because of the resemblance of the strips of paper to the tape of a Turing Machine, a small minority of children (possibly only Randall or some of his friends) pretended to be a Turing Machine by creating rules and executing them upon the tape of candy exactly like a real Turing Machine would do.
The title text refers to the fact that, although it would be hypothetically possible to create a Turing Machine that can only delete symbols, the information density of the tape would be greatly reduced, and the original Turing Machine could read and write from the tape it operated on.