This story has gained an unbelievable amount of coverage today, I'm truly blown away by the conversations it's created. Thank you to everyone who has offered advice and information on the app store review process, it's certainly been educational! Finding myself on the front page of MacRumours was a particularly shocking experience, so thanks for that one too.
After taking up @migrantp's advice and submitting an appeal for my rejection, Apple reviewed the app again and asked to schedule a call with me. I got a call from a lovely chap at Apple (I believe his name was Richard) who explained the situation to me.
Why it was rejected
The rejection was largely due to the inclusion of 3 categories in the categories tab. "Doctor Who", "Nigel Thornberry" and "Star Trek" are the root of the problem. Apple has particular issues with the copyright of these 3 categories which mean my app couldn't be approved.
The inclusion of images of Nigel Thornberry in the screenshots for the app were the secondary cause of the rejection.
Richard was extremely polite and helpful and I'm very grateful for the speed at which this has all progressed. I've been assured that if I resubmit after removing these categories that my app will be approved and I can get it back into the store.
It was also explained to me that the ability to search in the search tab for these images was not the problem, but pre-populating the search in the categories tab, is not allowed.
Richard said that in future if I run into issues with categories they will be sure to specify which categories are the issue rather than giving me a canned response.
I'm really happy to say that I've just ammended the categories and screenshots and that the app has been submitted for review.
Hopefully GIF Finder will be coming back to an App Store near you soon!
Now to finish that 3.0 update...