I disagree that they violated copyright. If they're using a screenshot or a short clip from a movie that is definitely fair use. On the other hand, what Giphy is doing is copying the entire meme.
What? That's absolutely not guaranteed to be fair use. AFAIK there's no precedent for such things. And even if random people making memes is fair use, Giphy would still be violating the copyright of the original media by hosting nearly unedited clips for commercial reasons. The vast, vast, vast majority of memes are not transformative.