according to its website, is "all about removing the obstacles that stand in the way of the education YOU want and deserve." We assume one of those obstacles is doing homework and that's why the company -- whose primary business appears to be buying and selling textbooks -- offers homework help (advertised to get you better grades and help you "get ready for the real world"). How true!
What they said. We're confused why the rep -- comparing your situation to a student posting a question from a book -- concluded that there was no reason to remove your question. It's true that many questions don't rise to the level of copyright protection because they're too short or because there are a limited number of ways to express the question (the merger doctrine) -- for example, "What are the primary themes in Jacobean literature?" or "What motivated Dwight Eisenhower to run for president?" But we see no reason why a longer question with sufficient detail -- for example, a bar exam hypothetical -- could not be protected under copyright. This would be true regardless of whether the question was pilfered from you, or written for a textbook.
Your challenge is twofold. You face two hurdles: (1) convincing Chegg that your question can be protected by copyright law (see above); and (2) getting Chegg to remove your question. You may be able to accomplish the latter through a DMCA notice via Chegg's IPR program. After all, according to Chegg's website, "if a professor reviews your notes and reports to Chegg that the notes do, in fact, violate their copyright, Chegg will remove the notes." If Chegg doesn't facilitate the removal, we assume you will find it cheaper to modify your questions than to hire a lawyer and threaten a lawsuit.