OP has clarified that OP's foreign-language kids
are moving to UK/US and wonder what they should say to indicate these things:
The factual answer (to that question is) there's no such term. (It's inconceivable a kid would use rubbings, erasings, debris, crumbs, etc.)
Kids just say "the eraser stuff" or "the stuff that came off when I erased."
OP, often with SWRs the correct and best answer is that in fact there is no such term in English.
Indeed, this is quite common among SWRs on the site.
It's important to realize that one can think of a good SWR to use for a given SWR puzzle, and that's a fun part of the game on the site. In the example at hand, one of the answers suggests "crumbs" and that's a fantastic/erudite idea, and I'd imagine that a handful of times someone has used that clever term.
(Indeed - it's a bit of a phenomenon in English, that certain fairly common things, actually annoyingly don't have words: so we use "whatsit" or "thingy" - indeed please review this astute question! )
So for this SWR in fact interestingly there is no common term.
That's the answer.
Everyone says "the little eraser thingies", "the purple bits that came off", "rubber bits", "eraser mess" etc.
The best you'll get are erudite/natty possibilities (the main purpose of this site after all!), or in some cases technical terms (cool to know, but not an answer to "the" currency word).
As a footnote, it occurred to me that: erasings works well. (I would probably use that if - for some astonishing reason - the issue had to be discussed extensively. Note that erasings (might as well call them that) physically include tiny bits of paper, lead, rubber, the blue ink from the rules, etc, they are not really "just bits of rubber", so for me "erasings" works.)
But please note that I only include "erasings" precisely as an example of the fact that, on all SWR questions, part of the sport is thinking up a really good word that "should" be the currency world. Erasings is not commonly used; I just "thought it up" purely on the basis: "since the answer is 'there is no such SWR' here's one I thought-up".