This depends largely on (like what Buffy commented) the circumstances and the grant. In my opinion, the circumstances may include where you are in your career. I see graduate students state declined fellowships on their CV relatively often, but I rarely see it on the CVs of professors who usually have enough (and usually more impressive) things on their CV.
But in terms of the grants, consider this example of the two of the most prestigious general graduate fellowships: the NSF GRP and the Ford Fellowship.
Both offer honorable mentions. It's pretty common to see graduate students state on their CVs that they got an honorable mention. However, suppose that a student received both the NSF GRP and Ford Fellowship in the same year. Because the Ford Fellowship prohibits one from having additional fellowships simultaneously, the student decides to decline the Ford Fellowship and accept the NSF GRP and reap the benefits of a much higher annual stipend as well. Should this student not state on their CV that they were accepted for the Ford Fellowship? What about a student who got the NSF GRP but only an honorable mention for the Ford Fellowship? Should this student be able to list both awards on their CV? It doesn't make sense (in my opinion) that the prior student should not be able to list the declined Ford Fellowship while the latter student should be able to list an honorable mention for the Ford Fellowship when an acceptance is clearly better than an honorable mention (discounting all the minority statuses that Ford takes into consideration).
However, that example was for two very prestigious fellowships. For minor grants/awards like travel grants, listing declined grants can be seen as 'padding the CV' since many travel grants/awards can be based on lottery rather than merit.
To sum it up, if the fellowship or grant is very prestigious, I see no reason as to why you shouldn't have a declined offer on your CV. However, if the fellowship or grant is minor or small, and your CV is already riddled with other awards or grants, then consider how it may be padding your CV with relatively trivial things that distract the reader from the more important fellowships/awards/grants. It's similar to why graduate students should consider deleting their undergraduate research symposium poster presentations from their CV as they progress in their academic career...
