This doesn't answer your question, but for the record, the CWGC site has a page explaining some of the abbreviations in their documents (scroll down), including those you can get from most casualty details pages:
https://www.cwgc.org/find-records/about-our-records/glossaryI think there used to be a link to this on each details page, but it's no longer there. The URL implies it should be mentioned on the About our Records page off Find Records, but it's not there either. I've been looking on the Wayback Machine, but so far can't see when it went.
Having said all that, CH isn't there, but my recollection is that the list was once longer.
You could ask the CWGC what CH means, and incidentally prompt them to make this useful page more visible. For example, some of the abbreviations give a clue as to whether to look for one of their distinctive headstones or whether it's more likely to be a private family monument, some of which are now in a parlous state, or even removed entirely in cemeteries' reuse of graves.